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① $7 = \\frac{9 + n}{3}$ ② $\\frac{-4 + x}{4} = 2$ ③ $2x - 6 = 30$ ④ $9…

Question

① $7 = \frac{9 + n}{3}$ ② $\frac{-4 + x}{4} = 2$ ③ $2x - 6 = 30$ ④ $9 = 9(-1 + x)$ ⑤ $6 = 3v + 3$ ⑥ $4 = b + b$ ⑦ $10 = 3 + 2b + 1$ ⑧ $4(4a - 4) = -128$ ⑨ $-6(2x - 2) = 108$ ⑩ $220 = -4(6m - 7)$ ⑪ $m - 4 = 8 - 5m$ ⑫ $6 - 4x = x - 4$ ⑬ $-5m - 6 = m - 6$ ⑭ $7x + 4(1 + 5x) = -30 - 7x$ ⑮ $5 + 4(x - 7) = -5x - 32$ ⑯ $9 - 31k = -3(1 + 5k)$

Explanation:

Response

Let's solve each equation one by one:

1. \( 7 = \frac{9 + n}{3} \)

Step 1: Multiply both sides by 3

\( 7 \times 3 = 9 + n \)
\( 21 = 9 + n \)

Step 2: Subtract 9 from both sides

\( 21 - 9 = n \)
\( n = 12 \)

2. \( \frac{-4 + x}{4} = 2 \)

Step 1: Multiply both sides by 4

\( -4 + x = 2 \times 4 \)
\( -4 + x = 8 \)

Step 2: Add 4 to both sides

\( x = 8 + 4 \)
\( x = 12 \)

3. \( 2x - 6 = 30 \)

Step 1: Add 6 to both sides

\( 2x = 30 + 6 \)
\( 2x = 36 \)

Step 2: Divide both sides by 2

\( x = \frac{36}{2} \)
\( x = 18 \)

4. \( 9 = 9(-1 + x) \)

Step 1: Divide both sides by 9

\( 1 = -1 + x \)

Step 2: Add 1 to both sides

\( x = 1 + 1 \)
\( x = 2 \)

5. \( 6 = 3v + 3 \)

Step 1: Subtract 3 from both sides

\( 6 - 3 = 3v \)
\( 3 = 3v \)

Step 2: Divide both sides by 3

\( v = \frac{3}{3} \)
\( v = 1 \)

6. \( 4 = b + b \)

Step 1: Combine like terms

\( 4 = 2b \)

Step 2: Divide both sides by 2

\( b = \frac{4}{2} \)
\( b = 2 \)

7. \( 10 = 3 + 2b + 1 \)

Step 1: Combine like terms

\( 10 = 4 + 2b \)

Step 2: Subtract 4 from both sides

\( 10 - 4 = 2b \)
\( 6 = 2b \)

Step 3: Divide both sides by 2

\( b = \frac{6}{2} \)
\( b = 3 \)

8. \( 4(4a - 4) = -128 \)

Step 1: Divide both sides by 4

\( 4a - 4 = \frac{-128}{4} \)
\( 4a - 4 = -32 \)

Step 2: Add 4 to both sides

\( 4a = -32 + 4 \)
\( 4a = -28 \)

Step 3: Divide both sides by 4

\( a = \frac{-28}{4} \)
\( a = -7 \)

9. \( -6(2x - 2) = 108 \)

Step 1: Divide both sides by -6

\( 2x - 2 = \frac{108}{-6} \)
\( 2x - 2 = -18 \)

Step 2: Add 2 to both sides

\( 2x = -18 + 2 \)
\( 2x = -16 \)

Step 3: Divide both sides by 2

\( x = \frac{-16}{2} \)
\( x = -8 \)

10. \( 220 = -4(6m - 7) \) (Assuming the left side is 220, maybe a typo)

Step 1: Divide both sides by -4

\( \frac{220}{-4} = 6m - 7 \)
\( -55 = 6m - 7 \)

Step 2: Add 7 to both sides

\( -55 + 7 = 6m \)
\( -48 = 6m \)

Step 3: Divide both sides by 6

\( m = \frac{-48}{6} \)
\( m = -8 \)

11. \( m - 4 = 8 - 5m \)

Step 1: Add 5m to both sides

\( m + 5m - 4 = 8 \)
\( 6m - 4 = 8 \)

Step 2: Add 4 to both sides

\( 6m = 8 + 4 \)
\( 6m = 12 \)

Step 3: Divide both sides by 6

\( m = \frac{12}{6} \)
\( m = 2 \)

12. \( 6 - 4x = x - 4 \)

Step 1: Add 4x to both sides

\( 6 = x + 4x - 4 \)
\( 6 = 5x - 4 \)

Step 2: Add 4 to both sides

\( 6 + 4 = 5x \)
\( 10 = 5x \)

Step 3: Divide both sides by 5

\( x = \frac{10}{5} \)
\( x = 2 \)

13. \( -5m - 6 = m - 6 \) (Assuming the right side is \( m - 6 \), maybe a typo)

Step 1: Add 5m to both sides

\( -6 = m + 5m - 6 \)
\( -6 = 6m - 6 \)

Step 2: Add 6 to both sides

\( 0 = 6m \)

Step 3: Divide both sides by 6

\( m = 0 \)

14. \( 7x + 4(1 + 5x) = -30 - 7x \)

Step 1: Distribute 4

\( 7x + 4 + 20x = -30 - 7x \)

Step 2: Combine like terms

\( 27x + 4 = -30 - 7x \)

Step 3: Add 7x to both sides

\( 27x + 7x + 4 = -30 \)
\( 34x + 4 = -30 \)

Step 4: Subtract 4 from both sides

\( 34x = -30 - 4 \)
\( 34x = -34 \)

Step 5: Divide both sides by 34

\( x = \frac{-34}{34} \)
\( x = -1 \)

15. \( 5 + 4(x - 7) = -5x - 32 \)

Step 1: Distribute 4

\( 5 + 4x - 28 = -5x - 32 \)

Step 2: Combine like terms

\( 4x - 23 = -5x - 32 \)

Step 3: Add 5x to both sides

\( 4x + 5x - 23 = -32 \)
\( 9x - 23 = -32 \)

Step 4: Add 23 to both sides

\( 9x = -32 + 23 \)
\( 9x = -9 \)

Step 5: Divide both sides by 9

\( x = \frac{-9}{9} \)
\( x = -1 \)

16. \( 9 - 31k = -3(1 + 5k) \) (Assuming the left side variable is \( k \), maybe a typo)

Step 1: Distribute -3

\( 9 - 31k = -3 - 15k \)

Step 2:…

Answer:

s:

  1. \( n = 12 \)
  2. \( x = 12 \)
  3. \( x = 18 \)
  4. \( x = 2 \)
  5. \( v = 1 \)
  6. \( b = 2 \)
  7. \( b = 3 \)
  8. \( a = -7 \)
  9. \( x = -8 \)
  10. \( m = -8 \) (assuming left side is 220)
  11. \( m = 2 \)
  12. \( x = 2 \)
  13. \( m = 0 \) (assuming right side is \( m - 6 \))
  14. \( x = -1 \)
  15. \( x = -1 \)
  16. \( k = \frac{3}{4} \) (assuming variable is \( k \))