Chapter 3.6, Problem 6STP

a. Solve the compound inequality $-4\le 3p-7<5.$

Show your work

b. Graph your solution.

To determine

To graph: the solution of given inequality and solve.

Explanation of Solution

Given information: $-4\le 3p-7<5$

Calculation: the inequality on number line find value for b and then plot the value on number line,

Add 7 on all sides,

  $\begin{array}{l}-4+7\le 3p-7+7<5+7\\ 3\le 3p<12\end{array}$

Divide by 3 on all the sides, and simplify,

  $\begin{array}{l}\frac{3}{3}\le \frac{3p}{3}<\frac{12}{3}\\ 1\le p<4\end{array}$

Therefore, the value of p is greater than or equal to 1 and less than 4.

Graph: Plot the value on number line,