Question

multi - step inequalities. solve each inequality and graph its solution.

1. (3x-5x + 2x)
2. (6x + 2+6x<14)
3. (-9 - 4p>-10)
4. (18geq5k + 4k)
5. (9geq - 2m+2 - 3)
6. (-3-6(4x + 6)>-111)
7. (6-4(6n + 7)geq122)
8. (-138geq - 6(6b - 7))
9. (167<6 + 7(2 - 7r))
10. (5(6 + 3r)+7geq127)
11. (-8x + 2x-16<-5x + 7x)
12. (-1-6x - 6>-11 - 7x)

Explanation:

5**

• \(30 + 15r+7\geq127\).
• Step 2: Combine like - terms
• Combine the constant terms: \(15r + 37\geq127\).
• Step 3: Subtract 37 from both sides
• \(15r+37 - 37\geq127 - 37\), resulting in \(15r\geq90\).
• Step 4: Divide both sides by 15
• \(\frac{15r}{15}\geq\frac{90}{15}\), so \(r\geq6\).

1. Solve the inequality \(-8x + 2x-16<-5x + 7x\):

• Step 1: Combine like - terms
• Combine the \(x\) terms on the left - hand side: \(-6x-16<2x\).
• Step 2: Add 6x to both sides
• \(-6x-16 + 6x<2x+6x\), resulting in \(-16<8x\).
• Step 3: Divide both sides by 8
• \(\frac{-16}{8}<\frac{8x}{8}\), so \(x>-2\).

1. Solve the inequality \(-1-6x-6>-11-7x\):

• Step 1: Combine like - terms
• Combine the constant terms on the left - hand side: \(-7-6x>-11-7x\).
• Step 2: Add 7x to both sides
• \(-7-6x + 7x>-11-7x+7x\), resulting in \(-7 + x>-11\).
• Step 3: Add 7 to both sides
• \(-7 + x+7>-11 + 7\), so \(x>-4\).

Answer:

1. \(x < 1\)
2. \(k\leq2\)
3. \(x < 3\)
4. \(n\leq - 6\)
5. \(b\geq5\)
6. \(r<-3\)
7. \(r\geq6\)
8. \(x>-2\)
9. \(x>-4\)