Chapter 3, Problem 23CT

To determine

To write: verbal sentence as an inequality and solve the inequality.

Answer to Problem 23CT

The verbal sentence can be written as $8\left(5+x\right)<56$ and the solution of the inequality is $x<2$

Explanation of Solution

Given information:

Eight times the sum of 5 and a number is less than 56.

Calculation:

Let $x$ be a number.

Therefore,

The sum of 5 and a number is $\left(5+x\right)$ .

Also,

8 times of $\left(5+x\right)$ is $8\left(5+x\right)$ .

Now, $8\left(5+x\right)$ is less than 56

  $\begin{array}{l}8\left(5+x\right)<56\text{ (Substitute) }\\ 40+8x<56\text{ (Use distributive law) }\\ 40+8x-40<56-40\text{ (Subtract 40 from each side)}\\ 8x<16\text{ (Simplify) }\\ \frac{8x}{8}<\frac{16}{8}\text{ (Divide each side by }8\text{) }\\ x<2\text{ (Simplify) }\end{array}$

Hence,

The verbal sentence can be written as $8\left(5+x\right)<56$ and the solution of the inequality is $x<2$