Question

Step 1: Multiply both sides by 8 To isolate the term with \(x\), multiply both sides of the equation by 8. \(\frac{x+2}{8}\cdot 8=4\cdot 8\) \(x+2=32\) Step 2: Subtract 2 from both sides Subtract 2 from both sides to solve for \(x\). \(x+2-2=32-2\) \(x=30\) Answer: \(x=30\) 2. Step 1: Multiply both sides by 9 To isolate the term with \(x\), multiply both sides of the equation by 9. \(\frac{x-10}{9}\cdot 9=7\cdot 9\) \(x-10=63\) Step 2: Add 10 to both sides Add 10 to both sides to solve for \(x\). \(x-10+10=63+10\) \(x=73\) Answer: \(x=73\) 3. Step 1: Divide both sides by 6 To isolate the term with \(x\), divide both sides of the equation by 6. \(\frac{6(x-11)}{6}=\frac{42}{6}\) \(x-11=7\) Step 2: Add 11 to both sides Add 11 to both sides to solve for \(x\). \(x-11+11=7+11\) \(x=18\) Answer: \(x=18\) 4. Step 1: Divide both sides by 4 To isolate the term with \(d\), divide both sides of the equation by 4. \(\frac{36}{4}=\frac{4(d-7)}{4}\) \(9=d-7\) Step 2: Add 7 to both sides Add 7 to both sides to solve for \(d\). \(9+7=d-7+7\) \(16=d\) Answer: \(d=16\)

Answer 1

All four solutions are correct. Quick summaries and checks:

1) Equation: (x + 2)/8 = 4
- Solve: x + 2 = 32 → x = 30
- Check: (30 + 2)/8 = 32/8 = 4 ✓

2) Equation: (x − 10)/9 = 7
- Solve: x − 10 = 63 → x = 73
- Check: (73 − 10)/9 = 63/9 = 7 ✓

3) Equation: 6(x − 11) = 42
- Solve: x − 11 = 7 → x = 18
- Check: 6(18 − 11) = 6·7 = 42 ✓

4) Equation: 4(d − 7) = 36
- Solve: d − 7 = 9 → d = 16
- Check: 4(16 − 7) = 4·9 = 36 ✓

Let me know if you want these shown with different methods or more practice problems.