Question

solve the following inequality and choose the correct graph that represents the answer. x - 3(x + 2) > 4

Explanation:

Step1: Expand the expression

$$\begin{align*} x-3(x + 2)&>4\\ x-(3x+6)&>4\\ x-3x - 6&>4 \end{align*}$$

Step2: Combine like terms

$$\begin{align*} x-3x-6&>4\\ -2x-6&>4 \end{align*}$$

Step3: Add 6 to both sides

$$\begin{align*} -2x-6 + 6&>4+6\\ -2x&>10 \end{align*}$$

Step4: Divide both sides by - 2 (and reverse the inequality sign)

$$\begin{align*} \frac{-2x}{-2}&<\frac{10}{-2}\\ x&<-5 \end{align*}$$

Answer:

The solution of the inequality \(x - 3(x + 2)>4\) is \(x<-5\). So the correct graph is the first one (the one with an open circle at \(-5\) and an arrow pointing to the left).