Question 812231: Solve: |6x+5|=|4x+3|
Enter a list of 2 mathematical expressions
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! When there is just one absolute value, you start by writing two equations, without absolute values, which would be equivalent. With two absolute values we will have to do this twice:
|6x+5| = |4x+3|
First we will write two equations, without the absolute value on the left:
6x+5 = |4x+3| or 6x+5 = -|4x+3|
Multiplying the each side of the second equation by -1:
6x+5 = |4x+3| or -6x-5 = |4x+3|
Next we will write two equations, without the absolute value, for each of the above equations:
6x+5 = 4x+3 or -(6x+5) = 4x+3 or -6x-5 = 4x+3 or -(-6x-5) = 4x+3
Now that the absolute values are gone, we can solve each of these:
6x+5 = 4x+3 or -6x-5 = 4x+3 or -6x-5 = 4x+3 or 6x+5 = 4x+3
2x+5 = 3 or -5 = 10x+3 = -3 or -5 = 10x+3 or 2x+5 = 3
2x = -2 or -8 = 10x or -8 = 10x or 2x = -2
x = -1 or -8/10 = x or -8/10 = x or x = -1
Reducing the fractions and eliminating the duplicates:
x = -1 or x = -4/5
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