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

Apr 29, 2015

We can divide both sides by 2 to get

$\left\mid x - 5 \right\mid > \frac{32}{2}$

$\to \left\mid x - 5 \right\mid > 16$

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

• Take any number $x > 21$

Say $x = 25$

Left hand side = $2 \cdot \left\mid 25 - 5 \right\mid = 2 \cdot 20 = 40$ ($> 32$)

• Take any number $x < - 11$

Say $x = - 12$

Left hand side = $2 \cdot \left\mid - 12 - 5 \right\mid = 2 \cdot \left\mid - 17 \right\mid = 2 \cdot 17 = 34$ ($> 32$)