3. $8z - 7 = 57$ \4. $11t - 16 = 39$ \5. $2m - 6 = 12 + 4$ \6. $3z + 4 = 22 - 3$ \solve and check. \7. $4x + 2 = 14$ \8. $7y - 6 = 8$ \9. $2x - 9 = 5$ \10. $8n - 13 = 3$ \11. $3t + 4 = 51 - 8$ \12. $2m - 15 = -21 + 8$ \solve and check. \13. $\frac{x}{5} + 3 = 7$ \14. $\frac{a}{5} + 6 = 11$ \15. $\frac{t}{3} + 9 = 12$ \16. $\frac{w}{11} - 2 = 7$

Question

3. $8z - 7 = 57$  \4. $11t - 16 = 39$  \5. $2m - 6 = 12 + 4$  \6. $3z + 4 = 22 - 3$  \solve and check. \7. $4x + 2 = 14$  \8. $7y - 6 = 8$  \9. $2x - 9 = 5$  \10. $8n - 13 = 3$  \11. $3t + 4 = 51 - 8$  \12. $2m - 15 = -21 + 8$  \solve and check. \13. $\frac{x}{5} + 3 = 7$  \14. $\frac{a}{5} + 6 = 11$  \15. $\frac{t}{3} + 9 = 12$  \16. $\frac{w}{11} - 2 = 7$

Accepted Answer

### Problem 3: $ 8z - 7 = 57 $
# Explanation:
## Step 1: Add 7 to both sides
To isolate the term with $ z $, we add 7 to both sides of the equation.
$ 8z - 7 + 7 = 57 + 7 $
$ 8z = 64 $

## Step 2: Divide by 8
To solve for $ z $, we divide both sides by 8.
$ \frac{8z}{8} = \frac{64}{8} $
$ z = 8 $

# Answer:
$ z = 8 $

### Problem 4: $ 11t - 16 = 39 $
# Explanation:
## Step 1: Add 16 to both sides
Add 16 to both sides to isolate the term with $ t $.
$ 11t - 16 + 16 = 39 + 16 $
$ 11t = 55 $

## Step 2: Divide by 11
Divide both sides by 11 to solve for $ t $.
$ \frac{11t}{11} = \frac{55}{11} $
$ t = 5 $

# Answer:
$ t = 5 $

### Problem 5: $ 2m - 6 = 12 + 4 $
# Explanation:
## Step 1: Simplify the right side
First, calculate the sum on the right side.
$ 12 + 4 = 16 $, so the equation becomes $ 2m - 6 = 16 $

## Step 2: Add 6 to both sides
Add 6 to both sides to isolate the term with $ m $.
$ 2m - 6 + 6 = 16 + 6 $
$ 2m = 22 $

## Step 3: Divide by 2
Divide both sides by 2 to solve for $ m $.
$ \frac{2m}{2} = \frac{22}{2} $
$ m = 11 $

# Answer:
$ m = 11 $

### Problem 6: $ 3z + 4 = 22 - 3 $
# Explanation:
## Step 1: Simplify the right side
Calculate the difference on the right side.
$ 22 - 3 = 19 $, so the equation becomes $ 3z + 4 = 19 $

## Step 2: Subtract 4 from both sides
Subtract 4 from both sides to isolate the term with $ z $.
$ 3z + 4 - 4 = 19 - 4 $
$ 3z = 15 $

## Step 3: Divide by 3
Divide both sides by 3 to solve for $ z $.
$ \frac{3z}{3} = \frac{15}{3} $
$ z = 5 $

# Answer:
$ z = 5 $

### Problem 7: $ 4x + 2 = 14 $ (Solve and Check)
# Explanation:
## Step 1: Subtract 2 from both sides
Subtract 2 from both sides to isolate the term with $ x $.
$ 4x + 2 - 2 = 14 - 2 $
$ 4x = 12 $

## Step 2: Divide by 4
Divide both sides by 4 to solve for $ x $.
$ \frac{4x}{4} = \frac{12}{4} $
$ x = 3 $

## Step 3: Check the solution
Substitute $ x = 3 $ back into the original equation:
Left side: $ 4(3) + 2 = 12 + 2 = 14 $
Right side: $ 14 $
Since left side = right side, $ x = 3 $ is correct.

# Answer:
$ x = 3 $

### Problem 8: $ 7y - 6 = 8 $ (Solve and Check)
# Explanation:
## Step 1: Add 6 to both sides
Add 6 to both sides to isolate the term with $ y $.
$ 7y - 6 + 6 = 8 + 6 $
$ 7y = 14 $

## Step 2: Divide by 7
Divide both sides by 7 to solve for $ y $.
$ \frac{7y}{7} = \frac{14}{7} $
$ y = 2 $

## Step 3: Check the solution
Substitute $ y = 2 $ back into the original equation:
Left side: $ 7(2) - 6 = 14 - 6 = 8 $
Right side: $ 8 $
Since left side = right side, $ y = 2 $ is correct.

# Answer:
$ y = 2 $

### Problem 9: $ 2x - 9 = 5 $ (Solve and Check)
# Explanation:
## Step 1: Add 9 to both sides
Add 9 to both sides to isolate the term with $ x $.
$ 2x - 9 + 9 = 5 + 9 $
$ 2x = 14 $

## Step 2: Divide by 2
Divide both sides by 2 to solve for $ x $.
$ \frac{2x}{2} = \frac{14}{2} $
$ x = 7 $

## Step 3: Check the solution
Substitute $ x = 7 $ back into the original equation:
Left side: $ 2(7) - 9 = 14 - 9 = 5 $
Right side: $ 5 $
Since left side = right side, $ x = 7 $ is correct.

# Answer:
$ x = 7 $

### Problem 10: $ 8n - 13 = 3 $ (Solve and Check)
# Explanation:
## Step 1: Add 13 to both sides
Add 13 to both sides to isolate the term with $ n $.
$ 8n - 13 + 13 = 3 + 13 $
$ 8n = 16 $

## Step 2: Divide by 8
Divide both sides by 8 to solve for $ n $.
$ \frac{8n}{8} = \frac{16}{8} $
$ n = 2 $

## Step 3: Check the solution
Substitute $ n = 2 $ back into the original equation:
Left side: $ 8(2) - 13 = 16 - 13 = 3 $
Right side: $ 3 $
Since left side = right side, $ n = 2 $ is correct.

# Answer:
$ n = 2 $

### Problem 11: $ 3t + 4 = 51 - 8 $ (Solve and Check)
# Explanation:
## Step 1: Simplify the right side
Calculate the difference on the right side.
$ 51 - 8 = 43 $, so the equation becomes $ 3t + 4 = 43 $

## Step 2: Subtract 4 from both sides
Subtract 4 from both sides to isolate the term with $ t $.
$ 3t + 4 - 4 = 43 - 4 $
$ 3t = 39 $

## Step 3: Divide by 3
Divide both sides by 3 to solve for $ t $.
$ \frac{3t}{3} = \frac{39}{3} $
$ t = 13 $

## Step 4: Check the solution
Substitute $ t = 13 $ back into the original equation:
Left side: $ 3(13) + 4 = 39 + 4 = 43 $
Right side: $ 51 - 8 = 43 $
Since left side = right side, $ t = 13 $ is correct.

# Answer:
$ t = 13 $

### Problem 12: $ 2m - 15 = -21 + 8 $ (Solve and Check)
# Explanation:
## Step 1: Simplify the right side
Calculate the sum on the right side.
$ -21 + 8 = -13 $, so the equation becomes $ 2m - 15 = -13 $

## Step 2: Add 15 to both sides
Add 15 to both sides to isolate the term with $ m $.
$ 2m - 15 + 15 = -13 + 15 $
$ 2m = 2 $

## Step 3: Divide by 2
Divide both sides by 2 to solve for $ m $.
$ \frac{2m}{2} = \frac{2}{2} $
$ m = 1 $

## Step 4: Check the solution
Substitute $ m = 1 $ back into the original equation:
Left side: $ 2(1) - 15 = 2 - 15 = -13 $
Right side: $ -21 + 8 = -13 $
Since left side = right side, $ m = 1 $ is correct.

# Answer:
$ m = 1 $

### Problem 13: $ \frac{x}{5} + 3 = 7 $ (Solve and Check)
# Explanation:
## Step 1: Subtract 3 from both sides
Subtract 3 from both sides to isolate the term with $ x $.
$ \frac{x}{5} + 3 - 3 = 7 - 3 $
$ \frac{x}{5} = 4 $

## Step 2: Multiply by 5
Multiply both sides by 5 to solve for $ x $.
$ 5 \times \frac{x}{5} = 4 \times 5 $
$ x = 20 $

## Step 3: Check the solution
Substitute $ x = 20 $ back into the original equation:
Left side: $ \frac{20}{5} + 3 = 4 + 3 = 7 $
Right side: $ 7 $
Since left side = right side, $ x = 20 $ is correct.

# Answer:
$ x = 20 $

### Problem 14: $ \frac{a}{5} + 6 = 11 $ (Solve and Check)
# Explanation:
## Step 1: Subtract 6 from both sides
Subtract 6 from both sides to isolate the term with $ a $.
$ \frac{a}{5} + 6 - 6 = 11 - 6 $
$ \frac{a}{5} = 5 $

## Step 2: Multiply by 5
Multiply both sides by 5 to solve for $ a $.
$ 5 \times \frac{a}{5} = 5 \times 5 $
$ a = 25 $

## Step 3: Check the solution
Substitute $ a = 25 $ back into the original equation:
Left side: $ \frac{25}{5} + 6 = 5 + 6 = 11 $
Right side: $ 11 $
Since left side = right side, $ a = 25 $ is correct.

# Answer:
$ a = 25 $

### Problem 15: $ \frac{t}{3} + 9 = 12 $ (Solve and Check)
# Explanation:
## Step 1: Subtract 9 from both sides
Subtract 9 from both sides to isolate the term with $ t $.
$ \frac{t}{3} + 9 - 9 = 12 - 9 $
$ \frac{t}{3} = 3 $

## Step 2: Multiply by 3
Multiply both sides by 3 to solve for $ t $.
$ 3 \times \frac{t}{3} = 3 \times 3 $
$ t = 9 $

## Step 3: Check the solution
Substitute $ t = 9 $ back into the original equation:
Left side: $ \frac{9}{3} + 9 = 3 + 9 = 12 $
Right side: $ 12 $
Since left side = right side, $ t = 9 $ is correct.

# Answer:
$ t = 9 $

### Problem 16: $ \frac{w}{11} - 2 = 7 $ (Solve and Check)
# Explanation:
## Step 1: Add 2 to both sides
Add 2 to both sides to isolate the term with $ w $.
$ \frac{w}{11} - 2 + 2 = 7 + 2 $
$ \frac{w}{11} = 9 $

## Step 2: Multiply by 11
Multiply both sides by 11 to solve for $ w $.
$ 11 \times \frac{w}{11} = 9 \times 11 $
$ w = 99 $

## Step 3: Check the solution
Substitute $ w = 99 $ back into the original equation:
Left side: $ \frac{99}{11} - 2 = 9 - 2 = 7 $
Right side: $ 7 $
Since left side = right side, $ w = 99 $ is correct.

# Answer:
$ w = 99 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 3: \( 8z - 7 = 57 \)

Step 1: Add 7 to both sides

Step 2: Divide by 8

Step 1: Add 16 to both sides

Step 2: Divide by 11

Step 1: Simplify the right side

Step 2: Add 6 to both sides

Step 3: Divide by 2

Answer:

Problem 4: \( 11t - 16 = 39 \)