Since the user options are all set to false, I will directly solve the problem and provide the final answer after working through it step by step.
Let’s go through each inequality one at a time, solve them carefully, and then match the correct solution with the number line shown in the image (even though we can’t see the image, we’ll assume the task is to solve each inequality correctly).
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Problem 1: Solve x + 5 > 9
Subtract 5 from both sides:
x + 5 - 5 > 9 - 5
→ x > 4
Solution: All numbers greater than 4. On a number line, this would be an open circle at 4 and shading to the right.
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Problem 2: Solve –3x ≤ 18
Divide both sides by –3. Remember: when dividing or multiplying by a negative number, flip the inequality sign!
–3x / –3 ≥ 18 / –3
→ x ≥ –6
Solution: All numbers greater than or equal to –6. Closed circle at –6, shading to the right.
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Problem 3: Solve 2x – 7 < 5
Add 7 to both sides:
2x – 7 + 7 < 5 + 7
→ 2x < 12
Divide by 2:
x < 6
Solution: Open circle at 6, shading to the left.
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Problem 4: Solve 4(x + 1) ≥ 20
First, distribute the 4:
4x + 4 ≥ 20
Subtract 4 from both sides:
4x ≥ 16
Divide by 4:
x ≥ 4
Solution: Closed circle at 4, shading to the right.
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Problem 5: Solve –2x + 3 > 11
Subtract 3 from both sides:
–2x > 8
Divide by –2 → flip the inequality:
x < –4
Solution: Open circle at –4, shading to the left.
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Problem 6: Solve 3x – 5 ≤ 10
Add 5 to both sides:
3x ≤ 15
Divide by 3:
x ≤ 5
Solution: Closed circle at 5, shading to the left.
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All problems solved. Now, since the original instruction was to “solve each inequality and graph its solution,” and assuming the student just needs the algebraic solutions (as no specific question about matching graphs is given), here are the answers:
Final Answer:
1. x > 4
2. x ≥ –6
3. x < 6
4. x ≥ 4
5. x < –4
6. x ≤ 5
Parent Tip: Review the logic above to help your child master the concept of solving inequalities worksheet kuta.
