SOLUTION: please help me slove this question .this is from california geometry book. : Solve each equation. and how did you slove it ? 1.) 6x - 42 = 4x 2.) 8 - 3n = -2 + 2n 3

Algebra ->  Equations -> SOLUTION: please help me slove this question .this is from california geometry book. : Solve each equation. and how did you slove it ? 1.) 6x - 42 = 4x 2.) 8 - 3n = -2 + 2n 3      Log On


   

Question 231066: please help me slove this question .this is from california geometry book.
: Solve each equation. and how did you slove it ?
1.) 6x - 42 = 4x
2.) 8 - 3n = -2 + 2n

3.) 3(y + 2) = -12 + y

4.) 12 + 7x = x - 18

5) 3x + 4 = 1 dividing by2x -5

6) 2 - 2x = 2 dividing by 3x -2

7)Mark bought 3 CDs and spent $24.
Write and solve an equation for the
average cost of each CD.


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please help me out . thank you in advance .











Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve each equation. and how did you solve it ?
:
We want to perform operations on both sides of the equation so we get the variable (x on the 1st one) by itself on one side
:
1.) 6x - 42 = 4x
Add 42 to both sides and we have
6x = 4x + 42
Subtract 4x from both sides
6x - 4x = 42
2x = 42
Divide both sides by x
x = 42%2F2
x = 21
:
Check solution in the original equation
6x - 42 = 4x
Replace x with 21
6(21) - 42 = 4(21)
126 - 42 = 84
84 = 84; equality! prove that x=21 is correct
:
:
2.) 8 - 3n = -2 + 2n
On this we will isolate n on the right, to keep it positive
Add 3n to both sides
8 = -2 + 2n + 3n
8 = -2 + 5n
add 2 to both sides
8 + 2 = 5n
10 = 5n
Divide both sides by 5
10%2F5 = n
n = 2
:
Prove this one n the original equation
8 - 3n = -2 + 2n
8 - 3(2) = -2 + 2(2)
8 - 6 = -2 + 4; equality!
:
:
3.) 3(y + 2) = -12 + y
Multiply both terms inside the brackets by 3, remove the brackets:
3y + 6 = -12 + y
subtract y from both sides
3y - y + 6 = -12
subtract 6 from both sides
2y = -12 - 6
2y = -18
divide both sides by 2
y = {{-9
:
Check solution. replace y with -9
3(-9 + 2) = -12 + (-9)
3(-7) = -12 - 9
-21 = -21!!
;
:
4.) 12 + 7x = x - 18
Subtract 12 from both sides
7x = x - 18 - 12
7x = x - 30
Subtract x from both sides
7x - x = -30
6x = -30
Divide both sides by 6
x = %28-30%29%2F6
x = -5
:
Check:
12 + 7(-5) = -5 - 18
12 - 35 = -23
-23 = -23!!
:
:
5) 3x + 4 = 1 dividing by2x -5
Assume the problem is:
%283x%2B4%29%2F%282x-5%29 = 1
Multiply both sides by (2x-5) to get rid of the denominator, we have:
3x + 4 = 1(2x - 5)
which is:
3x + 4 = 2x - 5
Subtract 4 from both sides
3x = 2x - 5 - 4
Subtract 2x from both sides
3x - 2x = -9
x = -9
:
See if that true, using the original equation
%283%28-9%29+%2B+4%29%2F%282%28-9%29+-+5%29 = 1
%28-27%2B4%29%2F%28-18-5%29 = 1
%28-23%29%2F%28-23%29 = 1
1 = 1!!
;
;
7)Mark bought 3 CDs and spent $24. Write and solve an equation for the
average cost of each CD.
Let c = cost of each CD
c = 24%2F3
c = $8 for each cd
;
Check: 3 * 8 = 24
:
:
If you study each one of these steps and understand, you will not have any
more trouble with these kind of problems. Important that you do this!