Questions on Algebra: Inequalities, trichotomy answered by real tutors!

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Algebra: Inequalities, trichotomy

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Question 241394: How do I solve:
7y-12 is less than 8y+5
Answer by jim_thompson5910(13794)

(Show Source):

You can put this solution on YOUR website!

Start with the given inequality.

Add

to both sides.

Subtract

from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by

to isolate

. note: Remember, the inequality sign flips when we divide both sides by a negative number.

Reduce.

----------------------------------------------------------------------

Answer:

So the solution is

Question 241404: I need help solving this question:
3(7-m) is less than or equal to 4(2-m)
Answer by jim_thompson5910(13794)

(Show Source):

You can put this solution on YOUR website!

Start with the given inequality.

Distribute.

Subtract

from both sides.

Add

to both sides.

Combine like terms on the left side.

Combine like terms on the right side.

----------------------------------------------------------------------

Answer:

So the solution is

Question 241389: How do I solve:
7y-12 is less than 8y+5
Answer by edjones(3296)

(Show Source):

You can put this solution on YOUR website!
7y-12 < 8y+5

add -7y-5 to each side.
y>-17
.
Ed

Question 241357: 1/2X+5>6 (NOTE IT IS GREATER THAN OR EQUAL TO
-
Found 2 solutions by unlockmath, Alan3354:
Answer by unlockmath(117)   (Show Source):
You can put this solution on YOUR website!
Hello,
First thing we want to do is get rid of the fraction so we multiply by 2 which gives us: Note:I'm assuming it is 1/2(x)
X+10>12 Now subtract 10 from both sides gives us:
X>or=2
RJ Toftness
www.math-unlock.com

Answer by Alan3354(6079)   (Show Source):
You can put this solution on YOUR website!
1/2X+5>=6
x + 10>=12
x>=2

Question 241007: help me solve -7x+15<27-4x
Answer by unlockmath(117)   (Show Source):
You can put this solution on YOUR website!
Hello,
First let's add 4x to both sides to look like this:
-7x+(4x)+15<27-4x+(4x)Combine like terms:
-3x+15<27 Now subtract 15 from both sides which gives us:
-3x<12 Now divide by -3 (Note when we divide by negative the < flips)
x>-4 There you go. Check the answer by using -3 and it should be correct.
RJ Toftness
www.math-unlock.com

Question 240894: What are the 2 kinds of inequalities?
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
less than [<] or less than or equal to [<=]
greater than [>] or greater than or equal to [>=]

Question 240849: 350+150p<=1800
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
350+150p<=1800
150P<=1,800-350
150P<=1,450
P<=1,450/150
P<=9.667 ANS.
PROOF:
LET P=9.6
350+150*9.6<=1,800
350+1,440<=1,800
1,790<=1,800

Question 240806: WHAT IS 4M>-1/3
Answer by JimboP1977(76)   (Show Source):
You can put this solution on YOUR website!
M > (-1/3)/4
M > (-1/3)*(1/4)
M > -1/12

Question 240495: whats the answer of this inequality 6x-4>26 then x >
Answer by unlockmath(117)   (Show Source):
You can put this solution on YOUR website!
Hello,
Let's first add 4 to both sides of the inequality which gives us:
6x is greater than 30 (Now divide both sides by 6)
x is greater than 5 (We got it. Any number greater than 5 will work in the inequality.
RJ Toftness
www.math-unlock.com

Question 240481: Solve The Inequality 6x<12
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
6x<12
x<12/6
x<2 ans.

Question 240460: how would you graph 5x + 3y is greater than or = to -9 usimg system of inequalities?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(5072)   (Show Source):
You can put this solution on YOUR website!

Step 1: Graph the equation . Since the original inequality has a symbol and therefore the solution set will contain points on the line, construct the graph using a solid line.

Step 2: Pick a test point that is NOT on the line. Since this line does not pass through the origin, the point (0,0) is an excellent choice.

Step 3: Substitute the coordinates from the point you selected in the previous step for the variables in your original inequality. Perform any necessary arithmetic.

Step 4: If the result of step 3 is a true statement, shade in the half-plane that contains the test point. If the result is a false statement, shade in the half-plane that does NOT contain the test point.

Your solution set is the shaded area. Since the line is solid, points on the line are included in the solution set.

John

Answer by stanbon(26274)   (Show Source):
You can put this solution on YOUR website!
how would you graph 5x + 3y is greater than or = to -9 using system of inequalities?
-----------------
1st: Graph the boundary line y = (-5/3)x - 3
-----------------

-----
Shade the half-plane ABOVE the boundary because
you want y GREATER than the boundary line.

===============================================
Cheers,
Stan H.

Question 240448: Suppose that tuition at a state college was $3500 per year in 1995 and has been increasing at a rate of $225 per year. Use this model to predict the tuition at this college in 2007.
Answer by stanbon(26274)   (Show Source):
You can put this solution on YOUR website!
Suppose that tuition at a state college was $3500 per year in 1995 and has been increasing at a rate of $225 per year. Use this model to predict the tuition at this college in 2007.
---------------------------------
T(x) = 225x + 3500 where x is the number of years after 1995
----------------------
2007 is 12 years after 1995
---------------
T(12) = 225*12 + 3500
T(12) = 2700 + 2500
T(12) = $5200
===================
Cheers,
Stan H.

Question 240440: I don't understand this problem, please help me, |j| minus 2 ≥ 6.
And another, -2 = |z| over 7.
p.s. the |z| over 7 stands for a fraction.
Answer by stanbon(26274)   (Show Source):
You can put this solution on YOUR website!
|j| minus 2 ≥ 6
---
|j| >= 8
---
j<= -8 or j>=8
========================

And another, -2 = |z| over 7
|z|/7 = -2
---
|z| = -14
---
There are no solutions because |z| cannot be negative.
=====================================================
Cheers,
Stan H.

Question 240432: i need help solving combined inequalities
like2>x+3>-8
Answer by vleith(1977)   (Show Source):
You can put this solution on YOUR website!
Solve each part separately first
break it up as
and
now solve each part

-->

Now plot them both and find where they are 'both true"
in this case, you would the numbers that satisfy both equations are

Question 240216: Please help me solve this problem 1/2x -5 <20
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!
We need to isolate the x to find the inequality.

Now we multiply by 2 on both sides to get rid of the fraction. So we get:

.
Note: if we had multiplied or divided on both sides of the inequality by a NEGATIVE number, the inequality symbol would have changed directions. But since we didn't, it remained the same.
.
Done! :)

Question 240181: let f(x)=|3-7x| find all x for which f(x) >_ 10
Answer by edjones(3296)   (Show Source):
You can put this solution on YOUR website!
|3-7x|>=10
.
3-7x>=10
-7x>=7
x>=-1
.
3-7x<=-10
-7x<=-13
x<=13/7
.
-1 .
Ed

Question 239727: where can i find free tutors to solve 3-6n-4<17?
Answer by edjones(3296)   (Show Source):
You can put this solution on YOUR website!
3-6n-4<17
6n<18
n<3
.
Ed

Question 239559: Ernest works in the shipping department loading shipping crates with boxes. each empty crate weighs 150 lb. how many boxes, each weighing 35 lb, can ernest put in the crate if the total weight is to be no more than 850 lb?
write an ineuality
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
150+35x<=850
35x<=850-150
35x<=700
x<=700/35
x<=20 boxes can be put in the crate.

Question 239530: How would I do this Algebra problem? "Three times the sum of a number and seven is greater than five times the number less thirteen?"
Answer by solver91311(5072)   (Show Source):
You can put this solution on YOUR website!

Let represent the number. Then the sum of a number an seven is: . Three times that is . Five times the number is , and less thirteen is then .

Put it all together:

Solve for the solution set interval. Remember to reverse the sense of the inequality if you multiply by a negative value.

John

Question 239216: the sum of two consecutive odd integers is 244. what is the smallest integer?
Answer by josmiceli(3007)   (Show Source):
You can put this solution on YOUR website!
Call the consecutive odd integers and
given:

---------------

The smallest integer is 121
check:

OK

Question 239110: solve the inequality:
y>-x+8
y<9/4x-5
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
y>-x+8 (red line)
y<9/4x-5 (green line)
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions -x +8 and 9x/4 -5).
Solution (4,4).
The area that meets these requirements is the area above the red line to the right of (4,4) and below the green line to the right of (4,4). Sorry don't have shadeing function.

Question 238245: 8(x+5)-6=18
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!
Hello. You submitted an equaiton under the title of inequality. I don't know if you chose the wrong title or if you used to wrong mathematical symbol. So, you need to verify that part.
.
We need to multiply 8 by the contents in the parenthesis, combine like terms, and solve for x.
.

<-- verify whether it should be eqn or inequality

Question 237965: 4(k-1)>4
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!

Question 237874: how do i solve this word problem (its really confusing)?
you take more than $8.25 but less than $10 to the amusement park. You ride the slide 15 times and decide that you need a soda. If the soda is $2,do you have enough money left over to buy the soda?

The key for this is as follows: The wetter than wet waterpark charges $0.75 to rent a mat plus $0.50 each time you ride the big water slide.

I have figured out that the equation is y=0.75+0.50x
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!
Equation:
.
You're very close. From this equation, we would say x is the amount of times you rode the slide and y would be the amount of money spent. So, if you rode the slide 15 times, the equation would then be:
.

y=8.25
.
If you only took somewhere between $8.25 and less than $10.00, would you have enought money to buy a $2 soda? No. Because you would only have left $1.25 at the most.

Question 238805: How do I solve 4x-7/8<-3 or 4x-7/8>6
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
4x-7/8<-3
4X<-3+7/8
4X<(-3*8+7)/8
4X<(-24+7)/8
4X<-17/8
X<(-17/8)/4
X<(-17/8)1/4
X<-17/8*4
X<-17/32 ANS.
-------------------------------
4x-7/8>6
4X>6+7/8
4X>(6*8+7)/8
4X>(48+7)/8
4X>55/8
X>(55/8)/4
X>(55/8)1/4
X>55/32 ANS.

Question 238835: Solve: 6x+2>7x-5
Im confused about how this answer is solved, my instructor is not available At the moment the multiple choice answers are A) {x|x<-3} B) {x|x<7} C) {x|x>-3} D){x|x>7} im not sure what this | bar means i think x is 7 but i may be wrong.
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
6x+2>7x-5
6X-7X>-5-2
-X>-7
X<-7/-1 (NOTE: WHEN DIVIDING BY A NEGATIVE VALUE THE > SIGN CHANGES TO A < SIGN.)
X<7 ANS. B)

Question 238809: How do I solve 4x-7/8<-3 or 4x-7/8>6
Answer by rfer(2688)   (Show Source):
You can put this solution on YOUR website!
4x-7/8<-3
32/8x-7/8<-24/8
32/8x<-17/8
x<(-17/8)/(32/8)
x<-17/8*8/32
x<-136/256
x<-17/32

Question 238526: Substitution method
6x+2y-4=0 and 10x+7y= -8
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!
To solve by substitution:
1. Leave first equation alone for now.
2. Solve for y on the second equation.
3. Plug in this value into the first eqn to find x
4. Once you know the x value, plug it again in the forst equation to find y.
.
Problem:

.

.

... now multiply by 7 to get rid of fraction

... now combine like terms

.

.
Here are your answers: and

Question 238606: how do you solve 0.9x(7x+6)is greater than or equal to 1.7-(x+6)?
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!
We may solve this using the decimals or multiply both sides by 10 in order to deal with just integers. I'll work both ways, you choose what is easier for you.
Problem:

.
With decimals:

same as to say...

.
If you multiply by 10:

Question 238581: Form a polynomial whose real zeros and degree are given.Type the answer in factored form with a leading coefficient of 1.
Zeros: -4, 4, 6; degree:3
Answer by user_dude2008(716)   (Show Source):
You can put this solution on YOUR website!
Answer: (x+4)(x-4)(x-6)

Question 238396: how do solve and graph -40 < -5r
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
-40 < -5r
-40/-5>R (NOTE: HE < SIGN CHANGES TO A > SIGN WHEN DIVIDING BY A NEGATIVE VALUE).
8>R
PROOF:
LET R=7.9
-40<-5*7.9
-40<-39.5

Question 238267: Ok, so I asked this question before but I need to know how you graph this.
Tell whether the given number is a solution of
5x–10>2x+4.
The numbers are
8, 5, 4, –2
How to graph this, please try the best you can, I'm really confused!!!
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
5x–10>2x+4
5X-2X>4+10
3X>14
X>14/3 ANS.
PROOF:
LET X=15/3
5*15/3-10>2*15/3+4
75/3-10>30/3+4
25-10>10+4
15>14

Question 238254: Tell whether the given number is a solution of
5x–10 > 2x+4.
The numbers are...
8, 5, 4, -2
Tell yes or no and graph.
Answer by solver91311(5072)   (Show Source):
You can put this solution on YOUR website!

Substitute the given numbers one at a time for the variable every place the variable appears. Then do the arithmetic. If you have a true statement, then the given number is a solution. If you have a false statement, then the given number is not a solution.

For example:

Is the answer to the question statement a yes or no?

John

Question 238202: -6 > g+4
Answer by nyc_function(260)   (Show Source):
You can put this solution on YOUR website!
-6 > g + 4
subtract 4 from both sides.
-6 - 4 > g
-10 > g
This means that whatever the value of g is it must be smaller than -10.

Question 238131: 2x+5<13
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website!
2x + 5 < 13,,,,,,,,,subtract 5 both sides
.
2x < 8,,,,,,,,,,,,divide both sides by 2
.
x<4,,,,,,,answer
.
.
check, let x =3,,,,,,,,2(3) + 5 < 13,,,,,,11<13,,,,ok
.

Question 238124: x+4>8
Found 2 solutions by College Student, nyc_function:
Answer by College Student(210)   (Show Source):
You can put this solution on YOUR website!
You may solve this problem in two small steps:
1. move 4 to the right of inequality by deducting it from both sides
2. now deduct 4 from 8
.
Problem:

.
Done! :)

Answer by nyc_function(260)   (Show Source):
You can put this solution on YOUR website!
x + 4 > 8
I assume that you want to solve for x.
Subract 4 from 8.
x > 8 - 4
x > 4
This means that whatever the value of x is, it must be greater than 4 in order to make the original inequality given a true statement.

Question 237538: Solve the system of equations by elimination.
5x – 2y = -4
4x – 7y = 3

Answer by stanbon(26274)   (Show Source):
You can put this solution on YOUR website!
Solve the system of equations by elimination.
5x – 2y = -4
4x – 7y = 3
-----------------------
Multiply the 1st eq. by 4 and the 2nd equation by 5 to get:
---
20x - 8y = -16
20x -35y = 15
------------------------
Subtract the 3nd Eq. from the 1st and solv for "y":
27y = - 31
y = -31/27
-----------------------
Substitute into 5x - 2y = -4 to solve for "x":
5x -2(-31/27) = -4
5x = -62/27 - (108/27)
5x = -170/27
x = -34/27
===================
Cheers,
Stan H

Question 237478: Solve the inequality:
4(6+x)>_ -2x
Answer by checkley77(7049)   (Show Source):
You can put this solution on YOUR website!
4(6+x)>_ -2x
24+4X>-2X
4X+2X>-24
6X>-24
X>-24/6
X>-4 ANS.
PROOF:
LET X=-3.9
4(6-3.9)>-2*-3.9
4(2.1)>7.8
8.4>7.8

Question 237367: I have a problem of -h is less then or equal to-14 and what I am trying to figure ot is do I need to divide the negative sign so that it's no longer there by h ?
Answer by Edwin McCravy(2922)   (Show Source):
You can put this solution on YOUR website!
I have a problem of -h is less then or equal to-14 and what I am trying to figure ot is do I need to divide the negative sign so that it's no longer there by h ?

There are two ways to do that. Here is the first way: Add 14 to both sides: Add h to both sides: That's the first way. Now here is the second way. It's shorter but it requires learning a rule. So learn this rule so you can use the shorter method. Rule: If you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality. Now divide both sides by and reverse the direction of the inequality: . ---------------- Notice that what we got using the first method is exactly the same as what we got using the second method . Edwin

Question 237344: A health official recommends a maximum cholesterol level of 200 units. By how many units must a patient with a cholesterol level of 275 units reduce her cholesterol level to satisfy the recommended maximum level???????
Answer by rapaljer(3620)   (Show Source):
You can put this solution on YOUR website!
275-200 = 75 units.

Check: If she is at 275 units and she reduces this by 75, the result is 200 which is the maximum recommended level.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Question 237248: What is the smallest value of x for which | x | < 6
Answer by ankor@dixie-net.com(6693)   (Show Source):
You can put this solution on YOUR website!
What is the smallest value of x for which | x | < 6
It would be x = -5

Question 237122: Solve the inequality:
5-x-2>3
Answer by rfer(2688)   (Show Source):
You can put this solution on YOUR website!
5-x-2>3
3-x>3
-x>1
x<-1