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Answer :
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!
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!
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