Question

question
solve for ( x ) and graph the solution on the number line below.
( x - 2 geq 10 )

Explanation:

Step1: Add 2 to both sides

To solve for \( x \) in the inequality \( x - 2 \geq 10 \), 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.

\[
x - 2 + 2 \geq 10 + 2
\]

Step2: Simplify both sides

Simplifying the left side, \( -2 + 2 = 0 \), so we have \( x \geq 12 \). On the right side, \( 10 + 2 = 12 \).

Answer:

The solution for \( x \) is \( x \geq 12 \). To graph this on a number line, we draw a closed circle at 12 (since the inequality is "greater than or equal to") and shade the line to the right of 12 to represent all numbers greater than or equal to 12.