QUESTION IMAGE
Question
in exercises 7 - 20, solve the inequality. graph the solution. (see examples 1 and 2.) 7. x - 4 < - 5 8. 1 ≤ s - 8 9. 6 ≥ m - 1 10. c - 12 > - 4 11. r + 4 < 5 12. - 8 ≤ 8 + y 13. 9 + w > 7 14. 15 ≥ q + 3 15. h - (- 2) ≥ 10 16. - 6 > t - (- 13) 17. j + 9 - 3 < 8 18. 1 - 12 + y ≥ - 5 19. 10 ≥ 3p - 2p - 7 20. 18 - 5z + 6z > 3 + 6
Response
- For the inequality \(x - 4<-5\):
- Step 1: Isolate the variable \(x\) by adding 4 to both sides
- According to the addition - property of inequalities, if \(a < b\), then \(a + c < b + c\). Here \(a=x - 4\), \(b=-5\), and \(c = 4\). So \(x-4 + 4<-5 + 4\).
- Simplifying gives \(x<-1\).
- For the inequality \(1\leq s - 8\):
- Step 1: Isolate the variable \(s\) by adding 8 to both sides
- Using the addition - property of inequalities, \(1+8\leq s - 8+8\).
- Simplifying gives \(9\leq s\) or \(s\geq9\).
- For the inequality \(6\geq m - 1\):
- Step 1: Isolate the variable \(m\) by adding 1 to both sides
- By the addition - property of inequalities, \(6 + 1\geq m-1 + 1\).
- Simplifying gives \(7\geq m\) or \(m\leq7\).
- For the inequality \(c - 12>-4\):
- Step 1: Isolate the variable \(c\) by adding 12 to both sides
- Using the addition - property of inequalities, \(c-12 + 12>-4 + 12\).
- Simplifying gives \(c>8\).
- For the inequality \(r + 4<5\):
- Step 1: Isolate the variable \(r\) by subtracting 4 from both sides
- According to the subtraction - property of inequalities, \(r+4-4<5 - 4\).
- Simplifying gives \(r<1\).
- For the inequality \(-8\leq8 + y\):
- Step 1: Isolate the variable \(y\) by subtracting 8 from both sides
- Using the subtraction - property of inequalities, \(-8-8\leq8 + y-8\).
- Simplifying gives \(-16\leq y\) or \(y\geq - 16\).
- For the inequality \(9 + w>7\):
- Step 1: Isolate the variable \(w\) by subtracting 9 from both sides
- By the subtraction - property of inequalities, \(9 + w-9>7 - 9\).
- Simplifying gives \(w>-2\).
- For the inequality \(15\geq q + 3\):
- Step 1: Isolate the variable \(q\) by subtracting 3 from both sides
- Using the subtraction - property of inequalities, \(15-3\geq q + 3-3\).
- Simplifying gives \(12\geq q\) or \(q\leq12\).
- For the inequality \(h-(-2)\geq10\):
- Step 1: Simplify the left - hand side
- Since \(h-(-2)=h + 2\), the inequality becomes \(h + 2\geq10\).
- Step 2: Isolate the variable \(h\) by subtracting 2 from both sides
- Using the subtraction - property of inequalities, \(h+2-2\geq10 - 2\).
- Simplifying gives \(h\geq8\).
- For the inequality \(-6>t-(-13)\):
- Step 1: Simplify the right - hand side
- Since \(t-(-13)=t + 13\), the inequality becomes \(-6>t + 13\).
- Step 2: Isolate the variable \(t\) by subtracting 13 from both sides
- Using the subtraction - property of inequalities, \(-6-13>t + 13-13\).
- Simplifying gives \(-19>t\) or \(t<-19\).
- For the inequality \(j + 9-3<8\):
- Step 1: Simplify the left - hand side
- \(j + 9-3=j + 6\), so the inequality is \(j + 6<8\).
- Step 2: Isolate the variable \(j\) by subtracting 6 from both sides
- Using the subtraction - property of inequalities, \(j+6-6<8 - 6\).
- Simplifying gives \(j<2\).
- For the inequality \(1-12 + y\geq - 5\):
- Step 1: Simplify the left - hand side
- \(1-12 + y=-11 + y\), so the inequality is \(-11 + y\geq - 5\).
- Step 2: Isolate the variable \(y\) by adding 11 to both sides
- Using the addition - property of inequalities, \(-11 + y+11\geq - 5+11\).
- Simplifying gives \(y\geq6\).
- For the inequality \(10\geq3p-2p - 7\):
- Step 1: Simplify the right - hand side
- Combine like terms: \(3p-2p=p\), so the inequality is \(10\geq p - 7\).
- **Step 2: Isolate the variable…
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