How do you solve |4x2|=|x+5|?

1 Answer
Apr 2, 2018

The solutions are S={1,75}

Explanation:

Let's build a sign chart

aaaaxaaaaaaaaaaaaaaaa12aaaaaaaaaa5aaaaaaaaa+

aaaa4x2aaaaaaaaaaaaa0aaaa+aaaaaaaa+

aaaax+5aaaaaa+aa#color(white)(aaaaaaaaa)+#aaaaa0aaa

aaaa|4x2|aaaaaa4x+2aa#color(white)(aaaa)4x-2#aaaaa4x2

aaaa|x+5|aaaaaaax5aa#color(white)(aaaa)x-5#aaaaax+5

Therefore,

In the interval x(,12)

4x+2=x5

5x=7

x=75

In the interval x(12,5)

4x2=x5

3x=3

x=1

In the interval x(5,+)

4x2=x+5

5x=7

x=75

Therefore,

the solutions are S={1,75}

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