Question

solve the equations. color the picture the appropriate color according to your answer. show all work.

1. $x - 8 = -14$ \hspace{3cm} red \hspace{2cm} 2. $5 = \frac{x}{20}$ \hspace{3cm} orange
2. $-15x = 135$ \hspace{2.5cm} yellow \hspace{1cm} 4. $-16 = x - 15$ \hspace{2.5cm} green
3. $-208 = 13x$ \hspace{2.2cm} light green \hspace{0.5cm} 6. $x - 7 = -11$ \hspace{3cm} blue
4. $3.5 = -0.7x$ \hspace{2.3cm} light blue \hspace{0.5cm} 8. $-5.6x = 56$ \hspace{3cm} purple
5. $32 = x + 18$ \hspace{2.7cm} tan \hspace{1.5cm} 10. $x - 3.2 = -9.1$ \hspace{2.8cm} pink
6. $1 = 7x + 1$ \hspace{2.7cm} red \hspace{1.5cm} 12. $-7x - 2 = 19$ \hspace{2.8cm} orange
7. $-2 = 3x - 5x$ \hspace{2.5cm} yellow \hspace{1cm} 14. $5 + 4x = -23$ \hspace{2.8cm} green
8. $-3x + 5 = -19$ \hspace{2.2cm} light green \hspace{0.5cm} 16. $13 = x + 9$ \hspace{3cm} blue
9. $21 = 10x + 1$ \hspace{2.7cm} light blue \hspace{1cm} 18. $-8x + 11 = -13$ \hspace{2.5cm} purple
10. $-3x + 3 = -33$ \hspace{2.5cm} tan \hspace{1.5cm} 20. $5x - 12 = 38$ \hspace{2.8cm} pink

Explanation:

Let's solve each equation step by step:

1. \( x - 8 = -14 \)

Step 1: Add 8 to both sides

\( x - 8 + 8 = -14 + 8 \)
\( x = -6 \)

2. \( 5 = \frac{x}{20} \)

Step 1: Multiply both sides by 20

\( 5 \times 20 = \frac{x}{20} \times 20 \)
\( x = 100 \)

3. \( -15x = 135 \)

Step 1: Divide both sides by -15

\( \frac{-15x}{-15} = \frac{135}{-15} \)
\( x = -9 \)

4. \( -16 = x - 15 \)

Step 1: Add 15 to both sides

\( -16 + 15 = x - 15 + 15 \)
\( x = -1 \)

5. \( -208 = 13x \)

Step 1: Divide both sides by 13

\( \frac{-208}{13} = \frac{13x}{13} \)
\( x = -16 \)

6. \( x - 7 = -11 \)

Step 1: Add 7 to both sides

\( x - 7 + 7 = -11 + 7 \)
\( x = -4 \)

7. \( 3.5 = -0.7x \)

Step 1: Divide both sides by -0.7

\( \frac{3.5}{-0.7} = \frac{-0.7x}{-0.7} \)
\( x = -5 \)

8. \( -5.6x = 56 \)

Step 1: Divide both sides by -5.6

\( \frac{-5.6x}{-5.6} = \frac{56}{-5.6} \)
\( x = -10 \)

9. \( 32 = x + 18 \)

Step 1: Subtract 18 from both sides

\( 32 - 18 = x + 18 - 18 \)
\( x = 14 \)

10. \( x - 3.2 = -9.1 \)

Step 1: Add 3.2 to both sides

\( x - 3.2 + 3.2 = -9.1 + 3.2 \)
\( x = -5.9 \)

11. \( 1 = 7x + 1 \)

Step 1: Subtract 1 from both sides

\( 1 - 1 = 7x + 1 - 1 \)
\( 0 = 7x \)

Step 2: Divide both sides by 7

\( \frac{0}{7} = \frac{7x}{7} \)
\( x = 0 \)

12. \( -7x - 2 = 19 \)

Step 1: Add 2 to both sides

\( -7x - 2 + 2 = 19 + 2 \)
\( -7x = 21 \)

Step 2: Divide both sides by -7

\( \frac{-7x}{-7} = \frac{21}{-7} \)
\( x = -3 \)

13. \( -2 = 3x - 5x \)

Step 1: Combine like terms

\( -2 = -2x \)

Step 2: Divide both sides by -2

\( \frac{-2}{-2} = \frac{-2x}{-2} \)
\( x = 1 \)

14. \( 5 + 4x = -23 \)

Step 1: Subtract 5 from both sides

\( 5 + 4x - 5 = -23 - 5 \)
\( 4x = -28 \)

Step 2: Divide both sides by 4

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

15. \( -3x + 5 = -19 \)

Step 1: Subtract 5 from both sides

\( -3x + 5 - 5 = -19 - 5 \)
\( -3x = -24 \)

Step 2: Divide both sides by -3

\( \frac{-3x}{-3} = \frac{-24}{-3} \)
\( x = 8 \)

16. \( 13 = x + 9 \)

Step 1: Subtract 9 from both sides

\( 13 - 9 = x + 9 - 9 \)
\( x = 4 \)

17. \( 21 = 10x + 1 \)

Step 1: Subtract 1 from both sides

\( 21 - 1 = 10x + 1 - 1 \)
\( 20 = 10x \)

Step 2: Divide both sides by 10

\( \frac{20}{10} = \frac{10x}{10} \)
\( x = 2 \)

18. \( -8x + 11 = -13 \)

Step 1: Subtract 11 from both sides

\( -8x + 11 - 11 = -13 - 11 \)
\( -8x = -24 \)

Step 2: Divide both sides by -8

\( \frac{-8x}{-8} = \frac{-24}{-8} \)
\( x = 3 \)

19. \( -3x + 3 = -33 \)

Step 1: Subtract 3 from both sides

\( -3x + 3 - 3 = -33 - 3 \)
\( -3x = -36 \)

Step 2: Divide both sides by -3

\( \frac{-3x}{-3} = \frac{-36}{-3} \)
\( x = 12 \)

20. \( 5x - 12 = 38 \)

Step 1: Add 12 to both sides

\( 5x - 12 + 12 = 38 + 12 \)
\( 5x = 50 \)

Step 2: Divide both sides by 5

\( \frac{5x}{5} = \frac{50}{5} \)
\( x = 10 \)

Final Answers:

1. \( \boldsymbol{x = -6} \)
2. \( \boldsymbol{x = 100} \)
3. \( \boldsymbol{x = -9} \)
4. \( \boldsymbol{x = -1} \)
5. \( \boldsymbol{x = -16} \)
6. \( \boldsymbol{x = -4} \)
7. \( \boldsymbol{x = -5} \)
8. \( \boldsymbol{x = -10} \)
9. \( \boldsymbol{x = 14} \)
10. \( \boldsymbol{x = -5.9} \)
11. \( \boldsymbol{x = 0} \)
12. \( \boldsymbol{x = -3} \)
13. \( \boldsymbol{x = 1} \)
14. \( \boldsymbol{x = -7} \)
15. \( \boldsymbol{x = 8} \)
16. \( \boldsymbol{x = 4} \)
17. \( \boldsymbol{x = 2} \)
18. \( \boldsymbol{x = 3} \)
19. \( \boldsymbol{x = 12} \)
20. \( \boldsymbol{x = 10} \)

Answer:

Let's solve each equation step by step:

1. \( x - 8 = -14 \)

Step 1: Add 8 to both sides

\( x - 8 + 8 = -14 + 8 \)
\( x = -6 \)

2. \( 5 = \frac{x}{20} \)

Step 1: Multiply both sides by 20

\( 5 \times 20 = \frac{x}{20} \times 20 \)
\( x = 100 \)

3. \( -15x = 135 \)

Step 1: Divide both sides by -15

\( \frac{-15x}{-15} = \frac{135}{-15} \)
\( x = -9 \)

4. \( -16 = x - 15 \)

Step 1: Add 15 to both sides

\( -16 + 15 = x - 15 + 15 \)
\( x = -1 \)

5. \( -208 = 13x \)

Step 1: Divide both sides by 13

\( \frac{-208}{13} = \frac{13x}{13} \)
\( x = -16 \)

6. \( x - 7 = -11 \)

Step 1: Add 7 to both sides

\( x - 7 + 7 = -11 + 7 \)
\( x = -4 \)

7. \( 3.5 = -0.7x \)

Step 1: Divide both sides by -0.7

\( \frac{3.5}{-0.7} = \frac{-0.7x}{-0.7} \)
\( x = -5 \)

8. \( -5.6x = 56 \)

Step 1: Divide both sides by -5.6

\( \frac{-5.6x}{-5.6} = \frac{56}{-5.6} \)
\( x = -10 \)

9. \( 32 = x + 18 \)

Step 1: Subtract 18 from both sides

\( 32 - 18 = x + 18 - 18 \)
\( x = 14 \)

10. \( x - 3.2 = -9.1 \)

Step 1: Add 3.2 to both sides

\( x - 3.2 + 3.2 = -9.1 + 3.2 \)
\( x = -5.9 \)

11. \( 1 = 7x + 1 \)

Step 1: Subtract 1 from both sides

\( 1 - 1 = 7x + 1 - 1 \)
\( 0 = 7x \)

Step 2: Divide both sides by 7

\( \frac{0}{7} = \frac{7x}{7} \)
\( x = 0 \)

12. \( -7x - 2 = 19 \)

Step 1: Add 2 to both sides

\( -7x - 2 + 2 = 19 + 2 \)
\( -7x = 21 \)

Step 2: Divide both sides by -7

\( \frac{-7x}{-7} = \frac{21}{-7} \)
\( x = -3 \)

13. \( -2 = 3x - 5x \)

Step 1: Combine like terms

\( -2 = -2x \)

Step 2: Divide both sides by -2

\( \frac{-2}{-2} = \frac{-2x}{-2} \)
\( x = 1 \)

14. \( 5 + 4x = -23 \)

Step 1: Subtract 5 from both sides

\( 5 + 4x - 5 = -23 - 5 \)
\( 4x = -28 \)

Step 2: Divide both sides by 4

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

15. \( -3x + 5 = -19 \)

Step 1: Subtract 5 from both sides

\( -3x + 5 - 5 = -19 - 5 \)
\( -3x = -24 \)

Step 2: Divide both sides by -3

\( \frac{-3x}{-3} = \frac{-24}{-3} \)
\( x = 8 \)

16. \( 13 = x + 9 \)

Step 1: Subtract 9 from both sides

\( 13 - 9 = x + 9 - 9 \)
\( x = 4 \)

17. \( 21 = 10x + 1 \)

Step 1: Subtract 1 from both sides

\( 21 - 1 = 10x + 1 - 1 \)
\( 20 = 10x \)

Step 2: Divide both sides by 10

\( \frac{20}{10} = \frac{10x}{10} \)
\( x = 2 \)

18. \( -8x + 11 = -13 \)

Step 1: Subtract 11 from both sides

\( -8x + 11 - 11 = -13 - 11 \)
\( -8x = -24 \)

Step 2: Divide both sides by -8

\( \frac{-8x}{-8} = \frac{-24}{-8} \)
\( x = 3 \)

19. \( -3x + 3 = -33 \)

Step 1: Subtract 3 from both sides

\( -3x + 3 - 3 = -33 - 3 \)
\( -3x = -36 \)

Step 2: Divide both sides by -3

\( \frac{-3x}{-3} = \frac{-36}{-3} \)
\( x = 12 \)

20. \( 5x - 12 = 38 \)

Step 1: Add 12 to both sides

\( 5x - 12 + 12 = 38 + 12 \)
\( 5x = 50 \)

Step 2: Divide both sides by 5

\( \frac{5x}{5} = \frac{50}{5} \)
\( x = 10 \)

Final Answers:

1. \( \boldsymbol{x = -6} \)
2. \( \boldsymbol{x = 100} \)
3. \( \boldsymbol{x = -9} \)
4. \( \boldsymbol{x = -1} \)
5. \( \boldsymbol{x = -16} \)
6. \( \boldsymbol{x = -4} \)
7. \( \boldsymbol{x = -5} \)
8. \( \boldsymbol{x = -10} \)
9. \( \boldsymbol{x = 14} \)
10. \( \boldsymbol{x = -5.9} \)
11. \( \boldsymbol{x = 0} \)
12. \( \boldsymbol{x = -3} \)
13. \( \boldsymbol{x = 1} \)
14. \( \boldsymbol{x = -7} \)
15. \( \boldsymbol{x = 8} \)
16. \( \boldsymbol{x = 4} \)
17. \( \boldsymbol{x = 2} \)
18. \( \boldsymbol{x = 3} \)
19. \( \boldsymbol{x = 12} \)
20. \( \boldsymbol{x = 10} \)