Question

Solve each inequality. Graph the solution set on a number line.

$3<d+5<8$.

Short answer

The solution of inequalities is $-2<d<3$.

Step-by-step solution

-Write the inequality and define compound inequality 

The inequality for the numbers is $3<d+5<8$.

A compound inequality containing the word ‘and’ is true if and only if both of the inequalities are true.

– Apply the definition of a compound inequality

Write the compound inequality as follows:

$\begin{array}{l}3<d+5<8\\ 3-5<d+5-5<8-5\\ -2<d<3\end{array}$

Therefore, the solution of each inequality is $-2<d$and $d<3$.

– Graph of the solution set 

The graph for the inequality $-2<d<3$ is as shown below