How do you solve |4x - 2| = | - x + 5|?

1 Answer
Apr 2, 2018

The solutions are S={-1, 7/5}

Explanation:

Let's build a sign chart

color(white)(aaaa)xcolor(white)(aaaaaaa)-oocolor(white)(aaaaaaaaa)1/2color(white)(aaaaaaaaaa)5color(white)(aaaaaaaaa)+oo

color(white)(aaaa)4x-2color(white)(aaaaaaa)-color(white)(aaaaaa)0color(white)(aaaa)+color(white)(aaaaaaaa)+

color(white)(aaaa)-x+5color(white)(aaaaaa)+color(white)(aa)#color(white)(aaaaaaaaa)+#color(white)(aaaaa)0color(white)(aaa)-

color(white)(aaaa)|4x-2|color(white)(aaaaaa)-4x+2color(white)(aa)#color(white)(aaaa)4x-2#color(white)(aaaaa)4x-2

color(white)(aaaa)|-x+5|color(white)(aaaaaaa)x-5color(white)(aa)#color(white)(aaaa)x-5#color(white)(aaaaa)-x+5

Therefore,

In the interval x in (-oo, 1/2)

-4x+2=x-5

5x=7

x=7/5

In the interval x in (1/2, 5)

4x-2=x-5

3x=-3

x=-1

In the interval x in (5, +oo)

4x-2=-x+5

5x=7

x=7/5

Therefore,

the solutions are S={-1, 7/5}

graph{(y-|4x-2|)(y-|-x+5|)=0 [-7.11, 8.69, -0.55, 7.35]}