Question

solve the following absolute value inequality.

\\|2x - 5| > 9\\

\\(x > ?\\) or \\(x < \\)

Explanation:

Set up the compound inequalities

An absolute value inequality of the form \(|u| > a\) (where \(a > 0\)) splits into a compound inequality using "or":

$$2x - 5 > 9 \quad \text{or} \quad 2x - 5 < -9$$

Solve the first inequality

Using the Solving Inequalities knowledge point:

$$
LATEXBLOCK0
$$

Solve the second inequality

Using the Solving Inequalities knowledge point:

$$
LATEXBLOCK1
$$

Combine the solution sets

Using the Compound Inequalities knowledge point, we combine the two individual solutions:

$$x > 7 \quad \text{or} \quad x < -2$$

Answer:

Solve the following absolute value inequality.

$$|2x - 5| > 9$$

\(x >\) <blank>7</blank> or \(x <\) <blank>-2</blank>