Chapter 6.1, Problem 48HP

To determine

Find the options which are not the same solution of the equation $2<x+5<10$

Answer to Problem 48HP

Option C and D are not the same solution of the equation $2<x+5<10$

Explanation of Solution

Given:

The sum of a number and 5 is between 2 and 10.

4 options are given:

  $\begin{array}{l}\text{A:}-3<x<5\\ \text{B:}2<x+5<10\\ \text{C:}7<x<15\\ \text{D:}-6<2x<10\end{array}$

Concept Used:

The inequality equation: $2<x+5<10$

Calculation:

The inequality equation: $2<x+5<10$

Solve for x:

  $\begin{array}{l}2<x+5<10\\ 2-5<x+5-5<10-5\\ -3<x<5\end{array}$ Solution: $-3<x<5$

Option C and D are not the same solution of the equation $2<x+5<10$

Thus, option C and D are not the same solution of the equation $2<x+5<10$