How do you solve $2abs(x -5) > 32$ ?

Question

1612 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-29T19:00:54

We can divide both sides by 2 to get

$abs(x-5) > 32/2$

$->abs(x-5) > 16$

This tells us two things:
Either $x - 5 > 16$ or $x-5<-16$

$x > 16 +5$ or $x < -16+5$

$color(green)(x>21$ or $color(green)(x<-11$

To verify your answer , choose appropriate values of $x$ and see if the inequality is satisfied

Say $x = 25$

Left hand side = $2*abs(25-5) = 2*20 = 40$ ( $>32$ )

Say $x = -12$

Left hand side = $2*abs(-12-5) = 2*abs(-17) = 2*17 = 34$ ( $>32$ )

How do you solve 2abs(x -5) > 32 2abs(x -5) > 32 ?