Match the inequality or equation to its solution.

1. [tex]x + 5 = 12[/tex]
2. [tex]x + 5 \textgreater 12[/tex]
3. [tex]x + 5 \textless 12[/tex]
4. [tex]x + 5 \geq 12[/tex]
5. [tex]x + 5 \leq 12[/tex]

Solutions:
A. [tex]x = 7[/tex]
B. Any number greater than 7
C. Any number less than 7
D. Any number greater than or equal to 7
E. Any number less than or equal to 7

Let's match each equation or inequality to its solution one by one:

1. Equation: [tex]$ x + 5 = 12 $[/tex]
- To solve for [tex]$ x $[/tex], we need to isolate it. We do this by subtracting 5 from both sides:
[tex]\[
x = 12 - 5
\][/tex]
[tex]\[
x = 7
\][/tex]
- Solution: 7

2. Inequality: [tex]$ x + 5 > 12 $[/tex]
- Again, we need to isolate [tex]$ x $[/tex]. We subtract 5 from both sides:
[tex]\[
x > 12 - 5
\][/tex]
[tex]\[
x > 7
\][/tex]
- Solution: Any number greater than 7

3. Inequality: [tex]$ x + 5 < 12 $[/tex]
- Subtract 5 from both sides to isolate [tex]$ x $[/tex]:
[tex]\[
x < 12 - 5
\][/tex]
[tex]\[
x < 7
\][/tex]
- Solution: Any number less than 7

4. Inequality: [tex]$ x + 5 \geq 12 $[/tex]
- Subtract 5 from both sides to solve for [tex]$ x $[/tex]:
[tex]\[
x \geq 12 - 5
\][/tex]
[tex]\[
x \geq 7
\][/tex]
- Solution: Any number greater than or equal to 7

5. Inequality: [tex]$ x + 5 \leq 12 $[/tex]
- Again, subtract 5 from both sides to find [tex]$ x $[/tex]:
[tex]\[
x \leq 12 - 5
\][/tex]
[tex]\[
x \leq 7
\][/tex]
- Solution: Any number less than or equal to 7

By following these steps, we matched each equation or inequality to the correct solution!