Chapter 5.4, Problem 47PFA

To determine

Find the inequality which Gianni has solved.

Answer to Problem 47PFA

Option is $\text{C:}16\ge 3a+4>1$ correct

Explanation of Solution

Given:

4 inequality equations are given and one solution:

  $\begin{array}{l}\text{A:}12\ge 3a+4>-3\\ \text{B:}12\ge 3a+4>1\\ \text{C:}16\ge 3a+4>1\\ \text{D:}16\ge 3a+4>-3\end{array}$ Solution: $-1<a\le 4$

Concept Used:

According to the graph the solution is $-1<a\le 4$

Calculation:

Solve each inequality separately and then choose the correct option.

Option A	Option B	Option C	Option D
$\begin{array}{l}12\ge 3a+4>-3\\ 12-4\ge 3a+4-4>-3-4\\ 8\ge 3a>-1\\ \frac{8}{3}\ge \frac{3a}{3}>\frac{-1}{3}\\ \frac{8}{3}\ge a>\frac{-1}{3}\end{array}$	$\begin{array}{l}12\ge 3a+4>1\\ 12-4\ge 3a+4-4>1-4\\ 8\ge 3a>-3\\ \frac{8}{3}\ge \frac{3a}{3}>\frac{-3}{3}\\ \frac{8}{3}\ge a>-1\end{array}$	$\begin{array}{l}16\ge 3a+4>1\\ 16-4\ge 3a+4-4>1-4\\ 12\ge 3a>-3\\ \frac{12}{3}\ge \frac{3a}{3}>\frac{-3}{3}\\ 4\ge a>-1\\ -1<a\le 4\end{array}$	$\begin{array}{l}16\ge 3a+4>-3\\ 16-4\ge 3a+4-4>-3-4\\ 12\ge 3a>-7\\ \frac{12}{3}\ge \frac{3a}{3}>\frac{-7}{3}\\ 4\ge a>\frac{-7}{3}\end{array}$

Thus, Option $\text{C:}16\ge 3a+4>1$ is correct.