Question

solve each equation.

1. $r + 11 = 3$
2. $n+7 = 13$
3. $d - 7 = 8$
4. $\frac{8}{5}a=-6$
5. $-\frac{p}{12}=6$
6. $\frac{x}{4}=8$
7. $\frac{12}{5}f=-18$
8. $\frac{y}{7}=-11$
9. $\frac{6}{7}y = 3$
10. $c - 14=-11$
11. $t - 14=-29$
12. $p - 21 = 52$
13. $b + 2=-5$
14. $q + 10 = 22$
15. $-12q = 84$
16. $5t = 30$
17. $5c - 7 = 8c - 4$
18. $2ell+6 = 6ell - 10$
19. $\frac{m}{10}+15 = 21$
20. $-\frac{m}{8}+7 = 5$
21. $8t + 1 = 3t - 19$
22. $9n + 4 = 5n+18$
23. $5c - 24=-4$
24. $3n + 7 = 28$
25. $-2y + 17=-13$
26. $-\frac{t}{13}-2 = 3$
27. $\frac{2}{9}x - 4=\frac{2}{3}$
28. $9 - 4g=-15$
29. $-4 - p=-2$
30. $21 - b = 11$
31. $-2(n + 7)=15$
32. $5(m - 1)=-25$
33. $-8a - 11 = 37$
34. $\frac{7}{4}q - 2=-5$
35. $2(5 - n)=8$
36. $-3(d - 7)=6$

0 preparing for geometry

Answer:

1. For the equation \(r + 11=3\):

• Explanation:
• Step1: Isolate the variable \(r\) by subtracting 11 from both sides
• \(r+11 - 11=3 - 11\)
• Step2: Simplify both sides
• \(r=3 - 11=-8\)
• Answer: \(r=-8\)

1. For the equation \(n + 7 = 13\):

• Explanation:
• Step1: Isolate the variable \(n\) by subtracting 7 from both sides
• \(n+7 - 7=13 - 7\)
• Step2: Simplify both sides
• \(n = 6\)
• Answer: \(n = 6\)

1. For the equation \(d-7 = 8\):

• Explanation:
• Step1: Isolate the variable \(d\) by adding 7 to both sides
• \(d-7 + 7=8 + 7\)
• Step2: Simplify both sides
• \(d=15\)
• Answer: \(d = 15\)

1. For the equation \(\frac{8}{5}a=-6\):

• Explanation:
• Step1: Solve for \(a\) by multiplying both sides by \(\frac{5}{8}\)
• \(a=-6\times\frac{5}{8}\)
• Step2: Simplify the right - hand side
• \(a=-\frac{30}{8}=-\frac{15}{4}\)
• Answer: \(a =-\frac{15}{4}\)

1. For the equation \(-\frac{p}{12}=6\):

• Explanation:
• Step1: Solve for \(p\) by multiplying both sides by - 12
• \(p=6\times(-12)\)
• Step2: Calculate the right - hand side
• \(p=-72\)
• Answer: \(p=-72\)

1. For the equation \(\frac{x}{4}=8\):

• Explanation:
• Step1: Solve for \(x\) by multiplying both sides by 4
• \(x = 8\times4\)
• Step2: Calculate the right - hand side
• \(x = 32\)
• Answer: \(x = 32\)

1. For the equation \(\frac{12}{5}f=-18\):

• Explanation:
• Step1: Solve for \(f\) by multiplying both sides by \(\frac{5}{12}\)
• \(f=-18\times\frac{5}{12}\)
• Step2: Simplify the right - hand side
• \(f=-\frac{90}{12}=-\frac{15}{2}\)
• Answer: \(f=-\frac{15}{2}\)

1. For the equation \(\frac{y}{7}=-11\):

• Explanation:
• Step1: Solve for \(y\) by multiplying both sides by 7
• \(y=-11\times7\)
• Step2: Calculate the right - hand side
• \(y=-77\)
• Answer: \(y=-77\)

1. For the equation \(\frac{6}{7}y = 3\):

• Explanation:
• Step1: Solve for \(y\) by multiplying both sides by \(\frac{7}{6}\)
• \(y=3\times\frac{7}{6}\)
• Step2: Simplify the right - hand side
• \(y=\frac{7}{2}\)
• Answer: \(y=\frac{7}{2}\)

1. For the equation \(c-14=-11\):

• Explanation:
• Step1: Isolate the variable \(c\) by adding 14 to both sides
• \(c-14 + 14=-11 + 14\)
• Step2: Simplify both sides
• \(c = 3\)
• Answer: \(c = 3\)

1. For the equation \(t-14=-29\):

• Explanation:
• Step1: Isolate the variable \(t\) by adding 14 to both sides
• \(t-14 + 14=-29+14\)
• Step2: Simplify both sides
• \(t=-15\)
• Answer: \(t=-15\)

1. For the equation \(p - 21=52\):

• Explanation:
• Step1: Isolate the variable \(p\) by adding 21 to both sides
• \(p-21 + 21=52 + 21\)
• Step2: Simplify both sides
• \(p = 73\)
• Answer: \(p = 73\)

1. For the equation \(b + 2=-5\):

• Explanation:
• Step1: Isolate the variable \(b\) by subtracting 2 from both sides
• \(b+2 - 2=-5 - 2\)
• Step2: Simplify both sides
• \(b=-7\)
• Answer: \(b=-7\)

1. For the equation \(q + 10=22\):

• Explanation:
• Step1: Isolate the variable \(q\) by subtracting 10 from both sides
• \(q+10 - 10=22 - 10\)
• Step2: Simplify both sides
• \(q = 12\)
• Answer: \(q = 12\)

1. For the equation \(-12q = 84\):

• Explanation:
• Step1: Solve for \(q\) by dividing both sides by - 12
• \(q=\frac{84}{-12}\)
• Step2: Simplify the right - hand side
• \(q=-7\)
• Answer: \(q=-7\)

1. For the equation \(5t = 30\):

• Explanation:
• Step1: Solve for \(t\) by dividing both sides by 5
• \(t=\frac{30}{5}\)
• Step2: Simplify the right - hand side
• \(t = 6\)
• Answer: \(t = 6\)

1. For the equation \(5c-7 = 8c-4\):

• Explanation:
• Step1: Move the terms with \(c\) to one side and constants to the other side
• \(5c-8c=-4 + 7\)
• Step2: Combine like terms
• \(-3c=3\)
• Step3: Solve for \(c\) by dividing both sides by - 3
• \(c=-1\)
• Answer: \(c=-1\)

1. For the equation \(2\ell+6 = 6\ell-10\):

• Explanation:
• Step1: Move the terms with \(\ell\) to one side and constants to the other side
• \(2\ell-6\ell=-10 - 6\)
• Step2: Combine like terms
• \(-4\ell=-16\)
• Step3: Solve for \(\ell\) by dividing both sides by - 4
• \(\ell = 4\)
• Answer: \(\ell = 4\)

1. For the equation \(\frac{m}{10}+15 = 21\):

• Explanation:
• Step1: Isolate the term with \(m\) by subtracting 15 from both sides
• \(\frac{m}{10}=21 - 15\)
• Step2: Simplify the right - hand side
• \(\frac{m}{10}=6\)
• Step3: Solve for \(m\) by multiplying both sides by 10
• \(m = 60\)
• Answer: \(m = 60\)

1. For the equation \(-\frac{m}{8}+7 = 5\):

• Explanation:
• Step1: Isolate the term with \(m\) by subtracting 7 from both sides
• \(-\frac{m}{8}=5 - 7=-2\)
• Step2: Solve for \(m\) by multiplying both sides by - 8
• \(m = 16\)
• Answer: \(m = 16\)

1. For the equation \(8t+1 = 3t-19\):

• Explanation:
• Step1: Move the terms with \(t\) to one side and constants to the other side
• \(8t-3t=-19 - 1\)
• Step2: Combine like terms
• \(5t=-20\)
• Step3: Solve for \(t\) by dividing both sides by 5
• \(t=-4\)
• Answer: \(t=-4\)

1. For the equation \(9n + 4=5n+18\):

• Explanation:
• Step1: Move the terms with \(n\) to one side and constants to the other side
• \(9n-5n=18 - 4\)
• Step2: Combine like terms
• \(4n=14\)
• Step3: Solve for \(n\) by dividing both sides by 4
• \(n=\frac{7}{2}\)
• Answer: \(n=\frac{7}{2}\)

1. For the equation \(5c-24=-4\):

• Explanation:
• Step1: Isolate the term with \(c\) by adding 24 to both sides
• \(5c=-4 + 24\)
• Step2: Simplify the right - hand side
• \(5c = 20\)
• Step3: Solve for \(c\) by dividing both sides by 5
• \(c = 4\)
• Answer: \(c = 4\)

1. For the equation \(3n+7 = 28\):

• Explanation:
• Step1: Isolate the term with \(n\) by subtracting 7 from both sides
• \(3n=28 - 7\)
• Step2: Simplify the right - hand side
• \(3n=21\)
• Step3: Solve for \(n\) by dividing both sides by 3
• \(n = 7\)
• Answer: \(n = 7\)

1. For the equation \(-2y+17=-13\):

• Explanation:
• Step1: Isolate the term with \(y\) by subtracting 17 from both sides
• \(-2y=-13 - 17\)
• Step2: Simplify the right - hand side
• \(-2y=-30\)
• Step3: Solve for \(y\) by dividing both sides by - 2
• \(y = 15\)
• Answer: \(y = 15\)

1. For the equation \(-\frac{t}{13}-2 = 3\):

• Explanation:
• Step1: Isolate the term with \(t\) by adding 2 to both sides
• \(-\frac{t}{13}=3 + 2\)
• Step2: Simplify the right - hand side
• \(-\frac{t}{13}=5\)
• Step3: Solve for \(t\) by multiplying both sides by - 13
• \(t=-65\)
• Answer: \(t=-65\)

1. For the equation \(\frac{2}{9}x-4=\frac{2}{3}\):

• Explanation:
• Step1: Isolate the term with \(x\) by adding 4 to both sides
• \(\frac{2}{9}x=\frac{2}{3}+4\)
• Step2: Make a common denominator for the right - hand side
• \(\frac{2}{9}x=\frac{2 + 12}{3}=\frac{14}{3}\)
• Step3: Solve for \(x\) by multiplying both sides by \(\frac{9}{2}\)
• \(x=\frac{14}{3}\times\frac{9}{2}=21\)
• Answer: \(x = 21\)

1. For the equation \(9-4g=-15\):

• Explanation:
• Step1: Isolate the term with \(g\) by subtracting 9 from both sides
• \(-4g=-15 - 9\)
• Step2: Simplify the right - hand side
• \(-4g=-24\)
• Step3: Solve for \(g\) by dividing both sides by - 4
• \(g = 6\)
• Answer: \(g = 6\)

1. For the equation \(-4-p=-2\):

• Explanation:
• Step1: Isolate the variable \(p\) by adding 4 to both sides
• \(-p=-2 + 4\)
• Step2: Simplify the right - hand side
• \(-p = 2\)
• Step3: Multiply both sides by - 1 to solve for \(p\)
• \(p=-2\)
• Answer: \(p=-2\)

1. For the equation \(21 - b=11\):

• Explanation:
• Step1: Isolate the variable \(b\) by subtracting 21 from both sides
• \(-b=11 - 21\)
• Step2: Simplify the right - hand side
• \(-b=-10\)
• Step3: Multiply both sides by - 1 to solve for \(b\)
• \(b = 10\)
• Answer: \(b = 10\)

1. For the equation \(-2(n + 7)=15\):

• Explanation:
• Step1: Distribute the - 2 on the left - hand side
• \(-2n-14 = 15\)
• Step2: Isolate the term with \(n\) by adding 14 to both sides
• \(-2n=15 + 14\)
• Step3: Simplify the right - hand side
• \(-2n=29\)
• Step4: Solve for \(n\) by dividing both sides by - 2
• \(n=-\frac{29}{2}\)
• Answer: \(n=-\frac{29}{2}\)

1. For the equation \(5(m - 1)=-25\):

• Explanation:
• Step1: Distribute the 5 on the left - hand side
• \(5m-5=-25\)
• Step2: Isolate the term with \(m\) by adding 5 to both sides
• \(5m=-25 + 5\)
• Step3: Simplify the right - hand side
• \(5m=-20\)
• Step4: Solve for \(m\) by dividing both sides by 5
• \(m=-4\)
• Answer: \(m=-4\)

1. **For the equation \