Russell Gillen

2021-12-10

Solve the absolute value equation for x.

$|x-\frac{2}{3}|=|6-x|$

Elaine Verrett

Beginner2021-12-11Added 41 answers

Step 1

Given equation is

$|x-\frac{2}{3}|=|6-x|$

Squaring both sides , we get

$(x-\frac{2}{3})}^{2}={(6-x)}^{2$

${x}^{2}-\frac{4}{3}x+\frac{4}{9}=36+{x}^{2}-12x$

$12x-\frac{4}{3}x+\frac{4}{9}-36=0$

108x-12x+4-324=0

96x-320=0

$x=\frac{320}{96}=\frac{10}{3}$

Step 2

Ans:

Solution of given equation is x=10/3

Given equation is

Squaring both sides , we get

108x-12x+4-324=0

96x-320=0

Step 2

Ans:

Solution of given equation is x=10/3