# How do you solve abs(2x+1) > 5?

May 2, 2015

$\left\mid 2 x + 1 \right\mid > 5$

The Absolute Value tells us how far the number is from Zero.

This tells us that :

Either $2 x + 1 > 5$ or $2 x + 1 < - 5$

$2 x > 5 - 1$ or $2 x < - 5 - 1$

$2 x > 4$ or $2 x < - 6$

color(green)(x>2 or color(green)(x < - 3

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

• Say $x = 4$ (A random number greater than 2)

Left hand side = $\left\mid 2 \cdot 4 + 1 \right\mid = \left\mid 8 + 1 \right\mid = \left\mid 9 \right\mid = 9$ ($> 5$)

• Say $x = - 6$(A random number less than -3)

Left hand side = $\left\mid 2 \cdot - 6 + 1 \right\mid = \left\mid - 12 + 1 \right\mid = \left\mid - 11 \right\mid = 11$ ($> 5$)