solve for a and graph the solution.
-2

Question

solve for a and graph the solution.
-2 < \frac{7a + 6}{4} \leq 5
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Accepted Answer

# Explanation:
## Step1: Multiply all parts by 4
$$
\begin{align*}
-2\times4&<\frac{7a + 6}{4}\times4\leq5\times4\
-8&<7a+6\leq20
\end{align*}
$$
## Step2: Subtract 6 from all parts
$$
\begin{align*}
-8 - 6&<7a+6-6\leq20 - 6\
-14&<7a\leq14
\end{align*}
$$
## Step3: Divide all parts by 7
$$
\begin{align*}
\frac{-14}{7}&<\frac{7a}{7}\leq\frac{14}{7}\
-2&<a\leq2
\end{align*}
$$

To graph: Place an open circle at $a = - 2$ (because the inequality is $ <$) and a closed circle at $a = 2$ (because the inequality is $\leq$), then draw a line segment connecting them.

# Answer:
The solution is $-2 < a\leq2$. On the number - line, there is an open circle at $-2$ and a closed circle at $2$ with a line segment between them.

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QUESTION IMAGE

Question

Explanation:

Step1: Multiply all parts by 4

Step2: Subtract 6 from all parts

Step3: Divide all parts by 7

Answer: