Q65. - Algebra 2

Question

Solve each inequality. (Lessons 1-5 and 1-6)

65. $\mathbf{5}<\mathbf{2}\mathbf{x}+\mathbf{7}<\mathbf{13}$

Step-by-Step Solution

Answer

The solution of the given inequality is $-1<x<3$.

Step 1 &ndash; State the concept

Solving an inequality means modifying the inequality so that the variable is isolated.

Step 2 &ndash; List the given data

The given inequality is $5<2x+7<13$.

Step 3 &ndash; Solve the inequality

$5<2x+7<13$  (Given inequality)

 

$5-7<2x+7-7<13-7$  (Subtract 7 from all terms of the inequality)

 

$-2<2x<6$  (Simplify)

 

$\frac{-2}{2}<\frac{2x}{2}<\frac{6}{2}$  (Divide all the terms of the inequality by 2)

 

$-1<x<3$ (Simplify)

 

So, the solution of the given inequality is $-1<x<3$.