Question

solve and graph. provide answers accurate to the nearest tenth.
|-4 + 9x| > 2
solution
graph
number line options

Explanation:

Step1: Solve the inequality \(| - 4 + 9x|>2\)

We know that if \(|u|>a\) (\(a>0\)), then \(u < - a\) or \(u>a\). Here \(u=-4 + 9x\) and \(a = 2\).
So we have two inequalities:

1. \(-4+9x<-2\)
2. \(-4 + 9x>2\)

Step2: Solve \(-4+9x<-2\)

Add \(4\) to both sides: \(9x<-2 + 4\), so \(9x<2\).
Divide both sides by \(9\): \(x<\frac{2}{9}\approx0.2\)

Step3: Solve \(-4 + 9x>2\)

Add \(4\) to both sides: \(9x>2 + 4\), so \(9x>6\).
Divide both sides by \(9\): \(x>\frac{6}{9}=\frac{2}{3}\approx0.7\)

Answer:

\(x<0.2\) or \(x > 0.7\)

To graph:

• Draw a number line.
• Place an open circle at \(x = 0.2\) (since \(x

eq0.2\)) and shade to the left of \(0.2\).

• Place an open circle at \(x=0.7\) (since \(x

eq0.7\)) and shade to the right of \(0.7\).