Question

solve the inequality. graph the solution set and write it in interval notation. 5(x + 1)-3 > -4(x - 5)+9. choose the correct graph below. a. graph of option a b. graph of option b c. graph of option c d. graph of option d write the answer in interval notation.

Explanation:

Step1: Expand the inequality

\[

$$\begin{align*} 5(x + 1)-3&>-4(x - 5)+9\\ 5x+5 - 3&>-4x + 20+9\\ 5x+2&>-4x+29 \end{align*}$$

\]

Step2: Add \(4x\) to both sides

\[

$$\begin{align*} 5x+4x + 2&>-4x+4x + 29\\ 9x+2&>29 \end{align*}$$

\]

Step3: Subtract 2 from both sides

\[

$$\begin{align*} 9x+2-2&>29 - 2\\ 9x&>27 \end{align*}$$

\]

Step4: Divide both sides by 9

\[

$$\begin{align*} \frac{9x}{9}&>\frac{27}{9}\\ x&>3 \end{align*}$$

\]
In interval - notation, the solution is \((3,\infty)\). The graph of the solution set has an open - circle at \(x = 3\) and an arrow pointing to the right.

Answer:

The solution in interval notation is \((3,\infty)\). The correct graph is one with an open - circle at \(x = 3\) and an arrow pointing to the right (assuming graph C is the one with an open - circle at 3 and arrow to the right).