Answer :
To solve the inequalities [tex]\(x - 2 \leq -7\)[/tex] or [tex]\(9 + x \geq 15\)[/tex], we can handle each inequality separately and then combine their results.
Step 1: Solve [tex]\(x - 2 \leq -7\)[/tex]
1. Start with the inequality:
[tex]\[
x - 2 \leq -7
\][/tex]
2. Add 2 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x - 2 + 2 \leq -7 + 2
\][/tex]
3. Simplify:
[tex]\[
x \leq -5
\][/tex]
Step 2: Solve [tex]\(9 + x \geq 15\)[/tex]
1. Start with the inequality:
[tex]\[
9 + x \geq 15
\][/tex]
2. Subtract 9 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
9 + x - 9 \geq 15 - 9
\][/tex]
3. Simplify:
[tex]\[
x \geq 6
\][/tex]
Step 3: Combine the solutions
Since the original problem uses "or" between the two inequalities, the combined solution includes the values of [tex]\(x\)[/tex] that satisfy either inequality.
- From the first inequality [tex]\(x \leq -5\)[/tex]
- From the second inequality [tex]\(x \geq 6\)[/tex]
So, the solution for the inequalities [tex]\(x - 2 \leq -7\)[/tex] or [tex]\(9 + x \geq 15\)[/tex] is:
[tex]\[
x \leq -5 \quad \text{or} \quad x \geq 6
\][/tex]
Therefore, the solution can be written as:
[tex]\[
x \leq -5 \text{ or } x \geq 6
\][/tex]
Step 1: Solve [tex]\(x - 2 \leq -7\)[/tex]
1. Start with the inequality:
[tex]\[
x - 2 \leq -7
\][/tex]
2. Add 2 to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
x - 2 + 2 \leq -7 + 2
\][/tex]
3. Simplify:
[tex]\[
x \leq -5
\][/tex]
Step 2: Solve [tex]\(9 + x \geq 15\)[/tex]
1. Start with the inequality:
[tex]\[
9 + x \geq 15
\][/tex]
2. Subtract 9 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
9 + x - 9 \geq 15 - 9
\][/tex]
3. Simplify:
[tex]\[
x \geq 6
\][/tex]
Step 3: Combine the solutions
Since the original problem uses "or" between the two inequalities, the combined solution includes the values of [tex]\(x\)[/tex] that satisfy either inequality.
- From the first inequality [tex]\(x \leq -5\)[/tex]
- From the second inequality [tex]\(x \geq 6\)[/tex]
So, the solution for the inequalities [tex]\(x - 2 \leq -7\)[/tex] or [tex]\(9 + x \geq 15\)[/tex] is:
[tex]\[
x \leq -5 \quad \text{or} \quad x \geq 6
\][/tex]
Therefore, the solution can be written as:
[tex]\[
x \leq -5 \text{ or } x \geq 6
\][/tex]
