a software - infinite pre-algebra
multi-step equations
solve each equation.
1) 6a + 5a = -11
2) -6n - 2n = 16
3) 4x + 6 + 3 = 17
4) 0 = -5n - 2n
5) 6r - 1 + 6r = 11
6) r + 11 + 8r = 29
7) -10 = -14v + 14v
8) -10p + 9p = 12
9) 42 = 8m + 13m
10) a - 2 + 3 = -2
11) 18 = 3(3x - 6)
12) 30 = -5(6n + 6)

Question

Accepted Answer

### Problem 1: $ 6a + 5a = -11 $
# Explanation:
## Step 1: Combine like terms
$ 6a + 5a = 11a $, so the equation becomes $ 11a = -11 $
## Step 2: Solve for $ a $
Divide both sides by 11: $ a = \frac{-11}{11} = -1 $
# Answer: $ a = -1 $

### Problem 2: $ -6n - 2n = 16 $
# Explanation:
## Step 1: Combine like terms
$ -6n - 2n = -8n $, so the equation becomes $ -8n = 16 $
## Step 2: Solve for $ n $
Divide both sides by -8: $ n = \frac{16}{-8} = -2 $
# Answer: $ n = -2 $

### Problem 3: $ 4x + 6 + 3 = 17 $
# Explanation:
## Step 1: Combine constant terms
$ 6 + 3 = 9 $, so the equation becomes $ 4x + 9 = 17 $
## Step 2: Subtract 9 from both sides
$ 4x = 17 - 9 = 8 $
## Step 3: Solve for $ x $
Divide both sides by 4: $ x = \frac{8}{4} = 2 $
# Answer: $ x = 2 $

### Problem 4: $ 0 = -5n - 2n $
# Explanation:
## Step 1: Combine like terms
$ -5n - 2n = -7n $, so the equation becomes $ 0 = -7n $
## Step 2: Solve for $ n $
Divide both sides by -7: $ n = \frac{0}{-7} = 0 $
# Answer: $ n = 0 $

### Problem 5: $ 6r - 1 + 6r = 11 $
# Explanation:
## Step 1: Combine like terms
$ 6r + 6r = 12r $, so the equation becomes $ 12r - 1 = 11 $
## Step 2: Add 1 to both sides
$ 12r = 11 + 1 = 12 $
## Step 3: Solve for $ r $
Divide both sides by 12: $ r = \frac{12}{12} = 1 $
# Answer: $ r = 1 $

### Problem 6: $ r + 11 + 8r = 29 $
# Explanation:
## Step 1: Combine like terms
$ r + 8r = 9r $, so the equation becomes $ 9r + 11 = 29 $
## Step 2: Subtract 11 from both sides
$ 9r = 29 - 11 = 18 $
## Step 3: Solve for $ r $
Divide both sides by 9: $ r = \frac{18}{9} = 2 $
# Answer: $ r = 2 $

### Problem 7: $ -10 = -14v + 14v $
# Explanation:
## Step 1: Combine like terms
$ -14v + 14v = 0 $, so the equation becomes $ -10 = 0 $
This is a contradiction, so there is no solution.
# Answer: No solution

### Problem 8: $ -10p + 9p = 12 $
# Explanation:
## Step 1: Combine like terms
$ -10p + 9p = -p $, so the equation becomes $ -p = 12 $
## Step 2: Solve for $ p $
Multiply both sides by -1: $ p = -12 $
# Answer: $ p = -12 $

### Problem 9: $ 42 = 8m + 13m $
# Explanation:
## Step 1: Combine like terms
$ 8m + 13m = 21m $, so the equation becomes $ 42 = 21m $
## Step 2: Solve for $ m $
Divide both sides by 21: $ m = \frac{42}{21} = 2 $
# Answer: $ m = 2 $

### Problem 10: $ a - 2 + 3 = -2 $
# Explanation:
## Step 1: Combine constant terms
$ -2 + 3 = 1 $, so the equation becomes $ a + 1 = -2 $
## Step 2: Subtract 1 from both sides
$ a = -2 - 1 = -3 $
# Answer: $ a = -3 $

### Problem 11: $ 18 = 3(3x - 6) $
# Explanation:
## Step 1: Distribute the 3
$ 3(3x - 6) = 9x - 18 $, so the equation becomes $ 18 = 9x - 18 $
## Step 2: Add 18 to both sides
$ 18 + 18 = 9x $ => $ 36 = 9x $
## Step 3: Solve for $ x $
Divide both sides by 9: $ x = \frac{36}{9} = 4 $
# Answer: $ x = 4 $

### Problem 12: $ 30 = -5(6n + 6) $
# Explanation:
## Step 1: Distribute the -5
$ -5(6n + 6) = -30n - 30 $, so the equation becomes $ 30 = -30n - 30 $
## Step 2: Add 30 to both sides
$ 30 + 30 = -30n $ => $ 60 = -30n $
## Step 3: Solve for $ n $
Divide both sides by -30: $ n = \frac{60}{-30} = -2 $
# Answer: $ n = -2 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 6a + 5a = -11 \)

Step 1: Combine like terms

Step 2: Solve for \( a \)

Step 1: Combine like terms

Step 2: Solve for \( n \)

Step 1: Combine constant terms

Step 2: Subtract 9 from both sides

Step 3: Solve for \( x \)

Answer:

Problem 2: \( -6n - 2n = 16 \)