Question

graph the solution to the inequality on the number line. $|x + 3|>7$

Explanation:

Step1: Solve the inequality

For \(|x + 3|>7\), we have two cases:

• Case 1: \(x+3>7\)

Subtract 3 from both sides: \(x+3 - 3>7 - 3\), so \(x>4\).

• Case 2: \(x + 3<-7\)

Subtract 3 from both sides: \(x+3-3<-7 - 3\), so \(x<-10\).

Step2: Graph on the number - line

• For \(x>4\), we draw an open circle at \(x = 4\) (because \(x = 4\) is not included in the solution) and shade to the right of \(4\).
• For \(x<-10\), we draw an open circle at \(x=-10\) (because \(x=-10\) is not included in the solution) and shade to the left of \(-10\).

Answer:

The solution of the inequality \(|x + 3|>7\) is \(x<-10\) or \(x>4\). On the number - line, we have an open circle at \(x=-10\) with shading to the left and an open circle at \(x = 4\) with shading to the right.