solve the equations. color the picture the appropriate color according to your answer. show all work.
1. $x - 8 = -14$ (red)
2. $5 = \frac{x}{20}$ (orange)
3. $-15x = 135$ (yellow)
4. $-16 = x - 15$ (green)
5. $-208 = 13x$ (light green)
6. $x - 7 = -11$ (blue)
7. $3.5 = -0.7x$ (light blue)
8. $-5.6x = 56$ (purple)
9. $32 = x + 18$ (tan)
10. $x - 3.2 = -9.1$ (pink)
11. $1 = 7x + 1$ (red)
12. $-7x - 2 = 19$ (orange)
13. $-2 = 3x - 5x$ (yellow)
14. $5 + 4x = -23$ (green)
15. $-3x + 5 = -19$ (light green)
16. $13 = x + 9$ (blue)
17. $21 = 10x + 1$ (light blue)
18. $-8x + 11 = -13$ (purple)
19. $-3x + 3 = -33$ (tan)
20. $5x - 12 = 38$ (pink)

Question

Accepted Answer

Let's solve some of these equations step by step. We'll pick a few to demonstrate the process.

### Equation 1: $ x - 8 = -14 $
# Explanation:
## Step 1: Add 8 to both sides
To isolate $ x $, we add 8 to both sides of the equation.
$ x - 8 + 8 = -14 + 8 $
## Step 2: Simplify both sides
Simplifying the left side: $ x - 8 + 8 = x $
Simplifying the right side: $ -14 + 8 = -6 $
So, $ x = -6 $
# Answer: $ x = -6 $

### Equation 2: $ 5 = \frac{x}{20} $
# Explanation:
## Step 1: Multiply both sides by 20
To solve for $ x $, we multiply both sides of the equation by 20.
$ 5 \times 20 = \frac{x}{20} \times 20 $
## Step 2: Simplify both sides
Simplifying the left side: $ 5 \times 20 = 100 $
Simplifying the right side: $ \frac{x}{20} \times 20 = x $
So, $ x = 100 $
# Answer: $ x = 100 $

### Equation 3: $ -15x = 135 $
# Explanation:
## Step 1: Divide both sides by -15
To isolate $ x $, we divide both sides of the equation by -15.
$ \frac{-15x}{-15} = \frac{135}{-15} $
## Step 2: Simplify both sides
Simplifying the left side: $ \frac{-15x}{-15} = x $
Simplifying the right side: $ \frac{135}{-15} = -9 $
So, $ x = -9 $
# Answer: $ x = -9 $

### Equation 4: $ -16 = x - 15 $
# Explanation:
## Step 1: Add 15 to both sides
To isolate $ x $, we add 15 to both sides of the equation.
$ -16 + 15 = x - 15 + 15 $
## Step 2: Simplify both sides
Simplifying the left side: $ -16 + 15 = -1 $
Simplifying the right side: $ x - 15 + 15 = x $
So, $ x = -1 $
# Answer: $ x = -1 $

### Equation 5: $ -208 = 13x $
# Explanation:
## Step 1: Divide both sides by 13
To isolate $ x $, we divide both sides of the equation by 13.
$ \frac{-208}{13} = \frac{13x}{13} $
## Step 2: Simplify both sides
Simplifying the left side: $ \frac{-208}{13} = -16 $
Simplifying the right side: $ \frac{13x}{13} = x $
So, $ x = -16 $
# Answer: $ x = -16 $

### Equation 6: $ x - 7 = -11 $
# Explanation:
## Step 1: Add 7 to both sides
To isolate $ x $, we add 7 to both sides of the equation.
$ x - 7 + 7 = -11 + 7 $
## Step 2: Simplify both sides
Simplifying the left side: $ x - 7 + 7 = x $
Simplifying the right side: $ -11 + 7 = -4 $
So, $ x = -4 $
# Answer: $ x = -4 $

### Equation 7: $ 3.5 = -0.7x $
# Explanation:
## Step 1: Divide both sides by -0.7
To isolate $ x $, we divide both sides of the equation by -0.7.
$ \frac{3.5}{-0.7} = \frac{-0.7x}{-0.7} $
## Step 2: Simplify both sides
Simplifying the left side: $ \frac{3.5}{-0.7} = -5 $
Simplifying the right side: $ \frac{-0.7x}{-0.7} = x $
So, $ x = -5 $
# Answer: $ x = -5 $

### Equation 8: $ -5.6x = 56 $
# Explanation:
## Step 1: Divide both sides by -5.6
To isolate $ x $, we divide both sides of the equation by -5.6.
$ \frac{-5.6x}{-5.6} = \frac{56}{-5.6} $
## Step 2: Simplify both sides
Simplifying the left side: $ \frac{-5.6x}{-5.6} = x $
Simplifying the right side: $ \frac{56}{-5.6} = -10 $
So, $ x = -10 $
# Answer: $ x = -10 $

### Equation 9: $ 32 = x + 18 $
# Explanation:
## Step 1: Subtract 18 from both sides
To isolate $ x $, we subtract 18 from both sides of the equation.
$ 32 - 18 = x + 18 - 18 $
## Step 2: Simplify both sides
Simplifying the left side: $ 32 - 18 = 14 $
Simplifying the right side: $ x + 18 - 18 = x $
So, $ x = 14 $
# Answer: $ x = 14 $

### Equation 10: $ x - 3.2 = -9.1 $
# Explanation:
## Step 1: Add 3.2 to both sides
To isolate $ x $, we add 3.2 to both sides of the equation.
$ x - 3.2 + 3.2 = -9.1 + 3.2 $
## Step 2: Simplify both sides
Simplifying the left side: $ x - 3.2 + 3.2 = x $
Simplifying the right side: $ -9.1 + 3.2 = -5.9 $
So, $ x = -5.9 $
# Answer: $ x = -5.9 $

### Equation 11: $ 1 = 7x + 1 $
# Explanation:
## Step 1: Subtract 1 from both sides
To isolate the term with $ x $, we subtract 1 from both sides of the equation.
$ 1 - 1 = 7x + 1 - 1 $
## Step 2: Simplify both sides
Simplifying the left side: $ 1 - 1 = 0 $
Simplifying the right side: $ 7x + 1 - 1 = 7x $
So, $ 0 = 7x $
## Step 3: Divide both sides by 7
To solve for $ x $, we divide both sides by 7.
$ \frac{0}{7} = \frac{7x}{7} $
Simplifying both sides: $ 0 = x $
So, $ x = 0 $
# Answer: $ x = 0 $

### Equation 12: $ -7x - 2 = 19 $
# Explanation:
## Step 1: Add 2 to both sides
To isolate the term with $ x $, we add 2 to both sides of the equation.
$ -7x - 2 + 2 = 19 + 2 $
## Step 2: Simplify both sides
Simplifying the left side: $ -7x - 2 + 2 = -7x $
Simplifying the right side: $ 19 + 2 = 21 $
So, $ -7x = 21 $
## Step 3: Divide both sides by -7
To solve for $ x $, we divide both sides by -7.
$ \frac{-7x}{-7} = \frac{21}{-7} $
Simplifying both sides: $ x = -3 $
# Answer: $ x = -3 $

### Equation 13: $ -2 = 3x - 5x $
# Explanation:
## Step 1: Combine like terms
First, combine the $ x $ terms on the right side.
$ 3x - 5x = -2x $
So the equation becomes $ -2 = -2x $
## Step 2: Divide both sides by -2
To solve for $ x $, we divide both sides by -2.
$ \frac{-2}{-2} = \frac{-2x}{-2} $
Simplifying both sides: $ 1 = x $
So, $ x = 1 $
# Answer: $ x = 1 $

### Equation 14: $ 5 + 4x = -23 $
# Explanation:
## Step 1: Subtract 5 from both sides
To isolate the term with $ x $, we subtract 5 from both sides of the equation.
$ 5 + 4x - 5 = -23 - 5 $
## Step 2: Simplify both sides
Simplifying the left side: $ 5 + 4x - 5 = 4x $
Simplifying the right side: $ -23 - 5 = -28 $
So, $ 4x = -28 $
## Step 3: Divide both sides by 4
To solve for $ x $, we divide both sides by 4.
$ \frac{4x}{4} = \frac{-28}{4} $
Simplifying both sides: $ x = -7 $
# Answer: $ x = -7 $

### Equation 15: $ -3x + 5 = -19 $
# Explanation:
## Step 1: Subtract 5 from both sides
To isolate the term with $ x $, we subtract 5 from both sides of the equation.
$ -3x + 5 - 5 = -19 - 5 $
## Step 2: Simplify both sides
Simplifying the left side: $ -3x + 5 - 5 = -3x $
Simplifying the right side: $ -19 - 5 = -24 $
So, $ -3x = -24 $
## Step 3: Divide both sides by -3
To solve for $ x $, we divide both sides by -3.
$ \frac{-3x}{-3} = \frac{-24}{-3} $
Simplifying both sides: $ x = 8 $
# Answer: $ x = 8 $

### Equation 16: $ 13 = x + 9 $
# Explanation:
## Step 1: Subtract 9 from both sides
To isolate $ x $, we subtract 9 from both sides of the equation.
$ 13 - 9 = x + 9 - 9 $
## Step 2: Simplify both sides
Simplifying the left side: $ 13 - 9 = 4 $
Simplifying the right side: $ x + 9 - 9 = x $
So, $ x = 4 $
# Answer: $ x = 4 $

### Equation 17: $ 21 = 10x + 1 $
# Explanation:
## Step 1: Subtract 1 from both sides
To isolate the term with $ x $, we subtract 1 from both sides of the equation.
$ 21 - 1 = 10x + 1 - 1 $
## Step 2: Simplify both sides
Simplifying the left side: $ 21 - 1 = 20 $
Simplifying the right side: $ 10x + 1 - 1 = 10x $
So, $ 20 = 10x $
## Step 3: Divide both sides by 10
To solve for $ x $, we divide both sides by 10.
$ \frac{20}{10} = \frac{10x}{10} $
Simplifying both sides: $ 2 = x $
So, $ x = 2 $
# Answer: $ x = 2 $

### Equation 18: $ -8x + 11 = -13 $
# Explanation:
## Step 1: Subtract 11 from both sides
To isolate the term with $ x $, we subtract 11 from both sides of the equation.
$ -8x + 11 - 11 = -13 - 11 $
## Step 2: Simplify both sides
Simplifying the left side: $ -8x + 11 - 11 = -8x $
Simplifying the right side: $ -13 - 11 = -24 $
So, $ -8x = -24 $
## Step 3: Divide both sides by -8
To solve for $ x $, we divide both sides by -8.
$ \frac{-8x}{-8} = \frac{-24}{-8} $
Simplifying both sides: $ x = 3 $
# Answer: $ x = 3 $

### Equation 19: $ -3x + 3 = -33 $
# Explanation:
## Step 1: Subtract 3 from both sides
To isolate the term with $ x $, we subtract 3 from both sides of the equation.
$ -3x + 3 - 3 = -33 - 3 $
## Step 2: Simplify both sides
Simplifying the left side: $ -3x + 3 - 3 = -3x $
Simplifying the right side: $ -33 - 3 = -36 $
So, $ -3x = -36 $
## Step 3: Divide both sides by -3
To solve for $ x $, we divide both sides by -3.
$ \frac{-3x}{-3} = \frac{-36}{-3} $
Simplifying both sides: $ x = 12 $
# Answer: $ x = 12 $

### Equation 20: $ 5x - 12 = 38 $
# Explanation:
## Step 1: Add 12 to both sides
To isolate the term with $ x $, we add 12 to both sides of the equation.
$ 5x - 12 + 12 = 38 + 12 $
## Step 2: Simplify both sides
Simplifying the left side: $ 5x - 12 + 12 = 5x $
Simplifying the right side: $ 38 + 12 = 50 $
So, $ 5x = 50 $
## Step 3: Divide both sides by 5
To solve for $ x $, we divide both sides by 5.
$ \frac{5x}{5} = \frac{50}{5} $
Simplifying both sides: $ x = 10 $
# Answer: $ x = 10 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Equation 1: \( x - 8 = -14 \)

Step 1: Add 8 to both sides

Step 2: Simplify both sides

Step 1: Multiply both sides by 20

Step 2: Simplify both sides

Step 1: Divide both sides by -15

Step 2: Simplify both sides

Answer:

Equation 2: \( 5 = \frac{x}{20} \)