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atomickitten
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Can someone (step-by-step) show me how to solve this absolute value equation? I'm having trouble understanding it.


|5y - 2| = |4y + 7|

Verified Answer :

ammm

Simplifying
5y + -2 = 4y + 7

Reorder the terms:
-2 + 5y = 4y + 7

Reorder the terms:
-2 + 5y = 7 + 4y

Solving
-2 + 5y = 7 + 4y

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4y' to each side of the equation.
-2 + 5y + -4y = 7 + 4y + -4y

Combine like terms: 5y + -4y = 1y
-2 + 1y = 7 + 4y + -4y

Combine like terms: 4y + -4y = 0
-2 + 1y = 7 + 0
-2 + 1y = 7

Add '2' to each side of the equation.
-2 + 2 + 1y = 7 + 2

Combine like terms: -2 + 2 = 0
0 + 1y = 7 + 2
1y = 7 + 2

Combine like terms: 7 + 2 = 9
1y = 9

Divide each side by '1'.
y = 9

Simplifying
y = 9

Int this problem you will have 3 equations since BOTH expressions are inside absolute values they can be equal IF they are both negative, both positive or one of each.
Setup as follows
5y - 2 = 4y + 7          5y - 2 = -(4y + 7)        -(5y - 2) = 4y + 7
5y = 4y + 9               5y - 2 = -4y - 7            -5y + 2 = 4y + 7
y = 9                         5y = -4y - 5                 -5y = 4y + 5
                                 9y = -5                        -9y = 5
                                 y = -5/9                        y = -5/9

We just have 2 solutions (since one repeated) of y = 9 and -5/9

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