Question

solve and graph the following inequality: -x + 2 < -2
provide an answer accurate to the nearest tenth.
inequality:
graph:
number line options

Explanation:

Step1: Subtract 2 from both sides

$$\begin{align*} -x+2-2&<-2 - 2\\ -x&<-4 \end{align*}$$

Step2: Multiply both sides by -1 (and reverse the inequality sign)

When multiplying or dividing an inequality by a negative number, the inequality sign flips.

$$\begin{align*} (-1)\times(-x)&>(-1)\times(-4)\\ x&>4 \end{align*}$$

Answer:

Inequality: \(x > 4\)

For the graph: On a number line, place an open circle at \(4\) (because \(4\) is not included in the solution set, since the inequality is \(x>4\)) and draw an arrow to the right of \(4\) to represent all the numbers greater than \(4\).