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Question 54348: I really need help in algebra 1. I do not understand problems such as -7x=-4x-27 or 1/2(12+x)=3/5(5x-15. Please help me i have a big test tommorow.
Found 2 solutions by checkley71, Edwin McCravy:
Answer by checkley71(8403)   (Show Source):
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website! I really need help in algebra 1. I do not understand problems
such as -7x=-4x-27 or 1/2(12+x)=3/5(5x-15). Please help me i have a big
test tommorow.
A more detailed version than above:
Here are the ten steps. Then I'll apply them to your equations:
1. Get rid of all fractions by multiplying all terms
on both sides by the LCD/1 of all the denominators that
appear in the equation.
2. Combine all like terms.
3. Get rid of all parentheses by using the distributive
principle.
4. Combine all like terms.
5. Get rid of all terms on the LEFT hand side which
DO NOT contain x (or whatever letter represents the unknown)
by adding their opposite to BOTH sides. Leave all terms alone on the LEFT
which DO contain x.
6. Combine all like terms.
7. Get rid of all terms on the RIGHT hand side which DO contain x (or whatever
letter represents the unknown) by adding their opposite to BOTH sides.
Leave all terms alone on the RIGHT which DO NOT contain x.
8. Combine all like terms.
9. Get rid of the numericxal coefficient of x by dividing both sides of the
equation by this coefficient.
10. Simplify the left side as just the unknown (x or whatever letter).
Simplify the right side as a single integer, fraction or decimal.
-----------------
Now I'll go through these 10 steps in each of your equations.
The first one skips the first 4
-7x = -4x - 27
1. Get rid of all fractions by multiplying all terms on both sides by
the LCD/1 of all the denominators that appear in the equation.
THERE ARE NO FRACTIONS, SO WE SKIP STEP 1.
2. Combine all like terms.
-7x = -4x - 27
THERE ARE NO LIKE TERMS ON EITHER SIDE. SO WE SKIP STEP 2.
3. Get rid of all parentheses by using the distributive principle.
-7x = -4x - 27
THERE ARE NO PARENTHESES, SO WE SKIP STEP 3.
4. Combine all like terms.
-7x = -4x - 27
THERE STILL ARE NO LIKE TERMS ON EITHER SIDE. SO WE SKIP STEP 2.
5. Get rid of all terms on the LEFT hand side which DO NOT contain x
(or whatever letter represents the unknown) by adding their opposite
to BOTH sides. Leave all terms alone on the LEFT which DO contain x.
-7x = -4x - 27
THERE IS JUST ONE TERM ON THE LEFT, -7x. IT CONTAINS x, SO WE JUST
LEAVE THAT ALONE.
6. Get rid of all terms on the RIGHT hand side which DO contain x (or
whatever letter represents the unknown) by adding their opposite to BOTH
sides. Leave all terms alone on the RIGHT which DO NOT contain x.
-7x = -4x - 27
FINALLY WE'VE GOTTEN TO A STEP WE CAN'T SKIP. The term -4x contains an x
and it is on the RIGHT, so we must add its opposite to both sides.
-7x = -4x - 27
+4x +4x
----------------
-3x = 0 - 27
7. Combine all like terms.
All we have to do is to combine 0 and -27, which is so trivial
we could have just done that in our heads and gotten
-3x = -27
8. Get rid of the numerical coefficient of x by dividing both
sides of the equation by this coefficient.
NOW WE DIVIDE BOTH SIDES BY THE NUMERICAL COEFFICIENT OF x, which is -3
-3x -27
----- = -----
-3 -3
10. Simplify the left side as just the unknown (x or whatever letter).
Simplify the right side as a single integer, fraction or decimal.
THE LEFT SIDE BECOMES JUST x, AND THE RIGHT SIDE IS FOUND BY DIVIDING
-27 BY -3 AND GETTING +9, WHICH WE CAN WRITE AS JUST 9, SO WE END UP WITH
x = 9
-------------------------------------------------
-------------------------------------------------
1 3
---(12+x) = ---(5x-15)
2 5
1. Get rid of all fractions by multiplying all terms on both sides
by the LCD/1 of all the denominators that appear in the equation.
THE LCD OF THE DENOMINATORS 2 AND 5 IS 10. PUT THAT OVER 1 AND
MULTIPLY BOTH SIDES BY IT:
10 1 10 3
--·---(12+x) = --·---(5x-15)
1 2 1 5
CANCEL THE 2 INTO THE 10 ON THE LEFT AND CANCEL THE 5 INTO THE
10 ON THE RIGHT:
5 2
10 1 10 3
--·---(12+x) = --·---(5x-15)
1 2 1 5
1 1
SO WE END UP WITH
5(12+x) = 6(5x-15)
2. Combine all like terms.
5(12+x) = 6(5x-15)
THERE ARE NONE TO COMBINE YET. WE CAN SKIP THIS STEP
3. Get rid of all parentheses by using the distributive principle.
5(12 + x) = 6(5x-15)
60 + 5x = 30x - 90
4. Combine all like terms.
THERE STILL ARE NONE TO COMBINE YET. WE CAN SKIP THIS STEP
5. Get rid of all terms on the LEFT hand side which DO NOT contain x
(or whatever letter represents the unknown) by adding their opposite
to BOTH sides. Leave all terms alone on the LEFT which DO contain x.
60 + 5x = 30x - 90
WE GET RID OF THE 60 ON THE LEFT BY ADDING -60 TO BOTH SIDES:
60 + 5x = 30x - 90
-60 -60
------------------------
0 + 5x = 30x - 150
6. Combine all like terms.
WE JUST COMBINE THE 0 and +5x as 5x
5x = 30x - 150
7. Get rid of all terms on the RIGHT hand side which DO contain x (or
whatever letter represents the unknown) by adding their opposite to
BOTH sides. Leave all terms alone on the RIGHT which DO NOT contain x.
5x = 30x - 150
WE GET RID OF THE 10x ON THE RIGHT BY ADDING -10x TO BOTH SIDES:
5x = 30x - 150
-30x -30x
-------------------
-25x = 0 - 150
8. Combine all like terms.
JUST COMBINE 0 and -150 AS -150
-25x = -150
9. Get rid of the numerical coefficient of x by dividing both sides of
the equation by this coefficient.
DIVIDE BOTH SIDES BY THE COEFFICIENT -25.
-25x -150
------ = ------
-25 -25
10. Simplify the left side as just the unknown (x or whatever letter).
Simplify the right side as a single integer, fraction or decimal.
THE LEFT SIDE BECOMES JUST x, AND THE RIGHT SIDE IS FOUND BY DIVIDING
-150 BY -25 AND GETTING +6, WHICH WE CAN WRITE AS JUST 6, SO WE END
UP WITH
x = 6
Edwin
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