Question

Solve the following compound
inequality. Enter your answer
using interval notation.
3 < 2x - 3 < 15

Answer 1

We are given the following compound inequality and want to find the values of x that makes this true:

$3<2x-3<15$

Add 3 to all parts of the inequality

$3\boxed{+3}<2x-3\boxed{+3}<15\boxed{+3}$

$6<2x<15$

Divide all parts of the inequality by 2

$6\boxed{\div 2}<2x\boxed{\div 2}<15\boxed{\div 2}$

$3<x<7.5$

Converting this into interval notation gives us:

$x:(3,7.5)$

Let me know if you need any clarifications, thanks!

~ Padoru