Solving Algebraic Equations worksheet with 10 problems requiring students to combine like terms and solve for variables.

Let's solve each of these algebraic equations step by step, combining like terms and isolating the variable.

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11. $ 2(3e - 2) + 9 = -5e $

Step 1: Distribute the 2
$ 6e - 4 + 9 = -5e $

Step 2: Combine like terms on the left
$ 6e + 5 = -5e $

Step 3: Add $ 5e $ to both sides
$ 11e + 5 = 0 $

Step 4: Subtract 5 from both sides
$ 11e = -5 $

Step 5: Divide by 11
$ e = -\frac{5}{11} $

✔ Answer: $ \boxed{e = -\frac{5}{11}} $

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12. $ 3(1 + p) = -5(p + 1) $

Step 1: Distribute
$ 3 + 3p = -5p - 5 $

Step 2: Add $ 5p $ to both sides
$ 3 + 8p = -5 $

Step 3: Subtract 3 from both sides
$ 8p = -8 $

Step 4: Divide by 8
$ p = -1 $

✔ Answer: $ \boxed{p = -1} $

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13. $ 3(1 - 3g) = -7 + g $

Step 1: Distribute
$ 3 - 9g = -7 + g $

Step 2: Add $ 9g $ to both sides
$ 3 = -7 + 10g $

Step 3: Add 7 to both sides
$ 10 = 10g $

Step 4: Divide by 10
$ g = 1 $

✔ Answer: $ \boxed{g = 1} $

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14. $ 1 + 2b = 4b + 9 $

Step 1: Subtract $ 2b $ from both sides
$ 1 = 2b + 9 $

Step 2: Subtract 9 from both sides
$ -8 = 2b $

Step 3: Divide by 2
$ b = -4 $

✔ Answer: $ \boxed{b = -4} $

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15. $ 2z + 6 = 3z + 1 $

Step 1: Subtract $ 2z $ from both sides
$ 6 = z + 1 $

Step 2: Subtract 1 from both sides
$ 5 = z $

✔ Answer: $ \boxed{z = 5} $

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16. $ 5a - 2 = -9a + 8 $

Step 1: Add $ 9a $ to both sides
$ 14a - 2 = 8 $

Step 2: Add 2 to both sides
$ 14a = 10 $

Step 3: Divide by 14
$ a = \frac{10}{14} = \frac{5}{7} $

✔ Answer: $ \boxed{a = \frac{5}{7}} $

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17. $ 6t - 5 = -9t - 9 $

Step 1: Add $ 9t $ to both sides
$ 15t - 5 = -9 $

Step 2: Add 5 to both sides
$ 15t = -4 $

Step 3: Divide by 15
$ t = -\frac{4}{15} $

✔ Answer: $ \boxed{t = -\frac{4}{15}} $

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18. $ -1 + 3f = -7 - 6f $

Step 1: Add $ 6f $ to both sides
$ -1 + 9f = -7 $

Step 2: Add 1 to both sides
$ 9f = -6 $

Step 3: Divide by 9
$ f = -\frac{6}{9} = -\frac{2}{3} $

✔ Answer: $ \boxed{f = -\frac{2}{3}} $

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19. $ 2 + r = 7 + 6r $

Step 1: Subtract $ r $ from both sides
$ 2 = 7 + 5r $

Step 2: Subtract 7 from both sides
$ -5 = 5r $

Step 3: Divide by 5
$ r = -1 $

✔ Answer: $ \boxed{r = -1} $

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20. $ -6k + 1 = -2 + 7k $

Step 1: Add $ 6k $ to both sides
$ 1 = -2 + 13k $

Step 2: Add 2 to both sides
$ 3 = 13k $

Step 3: Divide by 13
$ k = \frac{3}{13} $

✔ Answer: $ \boxed{k = \frac{3}{13}} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 11. $ e $ | $ -\frac{5}{11} $ |
| 12. $ p $ | $ -1 $ |
| 13. $ g $ | $ 1 $ |
| 14. $ b $ | $ -4 $ |
| 15. $ z $ | $ 5 $ |
| 16. $ a $ | $ \frac{5}{7} $ |
| 17. $ t $ | $ -\frac{4}{15} $ |
| 18. $ f $ | $ -\frac{2}{3} $ |
| 19. $ r $ | $ -1 $ |
| 20. $ k $ | $ \frac{3}{13} $ |

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