Question

solve the inequality. graph the solution - set and write it in interval notation. 5(x + 4)-1 > - 5(x - 1)+4. choose the correct graph below. a. graph a with arrow and - 1 marked b. graph b with arrow and - 1 marked c. graph c with arrow and - 1 marked d. graph d with arrow and - 1 marked write the answer in interval notation.

Explanation:

Step1: Expand the inequality

Expand \(5(x + 4)-1>-5(x - 1)+4\).
\[

$$\begin{align*} 5x+20 - 1&>-5x + 5+4\\ 5x+19&>-5x+9 \end{align*}$$

\]

Step2: Add \(5x\) to both sides

To get all \(x\) - terms on one side.
\[

$$\begin{align*} 5x+5x + 19&>-5x+5x + 9\\ 10x+19&>9 \end{align*}$$

\]

Step3: Subtract 19 from both sides

\[

$$\begin{align*} 10x+19-19&>9 - 19\\ 10x&>-10 \end{align*}$$

\]

Step4: Divide both sides by 10

\[

$$\begin{align*} \frac{10x}{10}&>\frac{-10}{10}\\ x&>- 1 \end{align*}$$

\]
In interval - notation, the solution is \((-1,\infty)\). The graph of the solution set is a number line with an open circle at \(-1\) and an arrow pointing to the right. So the correct graph is the one with an open - circle at \(-1\) and the arrow going to the right (assuming graph B is the one with an open - circle at \(-1\) and arrow to the right).

Answer:

The solution in interval notation is \((-1,\infty)\) and the correct graph is the one with an open - circle at \(-1\) and the arrow pointing to the right (if that is graph B).