To solve the inequality [tex]\( x - 2 < 7 \)[/tex], follow these steps:
1. Start with the given inequality:
[tex]\[
x - 2 < 7
\][/tex]
2. To isolate [tex]\( x \)[/tex], add 2 to both sides of the inequality. This step is performed to cancel out the [tex]\(-2\)[/tex] on the left side:
[tex]\[
x - 2 + 2 < 7 + 2
\][/tex]
3. Simplify both sides of the inequality. On the left side, [tex]\(-2 + 2\)[/tex] cancels out, leaving just [tex]\( x \)[/tex], and on the right side, [tex]\( 7 + 2 \)[/tex] equals 9:
[tex]\[
x < 9
\][/tex]
Therefore, the solution to the inequality [tex]\( x - 2 < 7 \)[/tex] is:
[tex]\[
x < 9
\][/tex]
