Question

solve the linear inequality. then write the solution in set - builder notation.
$x - 2 \geq 5$

Explanation:

Step1: Add 2 to both sides

To solve for \( x \) in the inequality \( x - 2 \geq 5 \), we add 2 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the direction of the inequality remains the same.
\[
x - 2 + 2 \geq 5 + 2
\]

Step2: Simplify both sides

Simplifying the left - hand side, \( x-2 + 2=x \). Simplifying the right - hand side, \( 5 + 2 = 7 \). So we get \( x\geq7 \).

Answer:

The solution in set - builder notation is \( \{x|x\geq7\} \)