Chapter 4, Problem 21CCSR

To determine

To identify: The values of x that makes both inequalities true

Answer to Problem 21CCSR

  $-6<x<7$

Explanation of Solution

Given information: Two inequalities are

  $\begin{array}{l}3x<4x+6\\ 2x+1<15\end{array}$

Calculation:

Solve each inequality for x and find the intersection of both inequalities

  $\begin{array}{l}3x<4x+6\\ 3x-4x<4x-4x+6\\ -x<6\\ x>-6\end{array}$

  $\begin{array}{l}2x+1<15\\ 2x+1-1<15-1\\ 2x<14\\ x<7\end{array}$

Now combine both inequalities and find the intersection

  $x>-6$ and $x<7$

  $-6<x<7$