Let's solve each equation step by step to find the value of the variable.
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1) 4a = 36
Divide both sides by 4:
$ a = \frac{36}{4} = 9 $
✔ a = 9
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2) b – 14 = 35
Add 14 to both sides:
$ b = 35 + 14 = 49 $
✔ b = 49
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3) 9c = 45
Divide both sides by 9:
$ c = \frac{45}{9} = 5 $
✔ c = 5
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4) 30 – d = 11
Subtract 30 from both sides:
$ -d = 11 - 30 = -19 $
Multiply both sides by -1:
$ d = 19 $
✔ d = 19
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5) e + 120 = 500
Subtract 120 from both sides:
$ e = 500 - 120 = 380 $
✔ e = 380
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6) 6f = 240
Divide both sides by 6:
$ f = \frac{240}{6} = 40 $
✔ f = 40
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7) ½ g = 12
Multiply both sides by 2:
$ g = 12 \times 2 = 24 $
✔ g = 24
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8) 24 – h = 9
Subtract 24 from both sides:
$ -h = 9 - 24 = -15 $
Multiply by -1:
$ h = 15 $
✔ h = 15
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9) 8i = 400
Divide both sides by 8:
$ i = \frac{400}{8} = 50 $
✔ i = 50
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10) 0.4 + j = 1
Subtract 0.4 from both sides:
$ j = 1 - 0.4 = 0.6 $
✔ j = 0.6
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11) 0.5k = 7
Divide both sides by 0.5 (or multiply by 2):
$ k = \frac{7}{0.5} = 14 $
✔ k = 14
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12) l – 0.7 = 1.5
Add 0.7 to both sides:
$ l = 1.5 + 0.7 = 2.2 $
✔ l = 2.2
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13) ⅓ m = 6
Multiply both sides by 3:
$ m = 6 \times 3 = 18 $
✔ m = 18
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14) n + 3⅕ = 12
Convert mixed number: $ 3\frac{1}{5} = \frac{16}{5} = 3.2 $
So:
$ n = 12 - 3.2 = 8.8 $
Or as a fraction:
$ 12 - \frac{16}{5} = \frac{60}{5} - \frac{16}{5} = \frac{44}{5} = 8\frac{4}{5} $
✔ n = 8.8 or 8⅘
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15) 2.3 – o = 0.5
Subtract 2.3 from both sides:
$ -o = 0.5 - 2.3 = -1.8 $
Multiply by -1:
$ o = 1.8 $
✔ o = 1.8
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16) 4p = 6
Divide both sides by 4:
$ p = \frac{6}{4} = 1.5 $
✔ p = 1.5
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17) 0.38 + q = 1
Subtract 0.38 from both sides:
$ q = 1 - 0.38 = 0.62 $
✔ q = 0.62
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18) 5r = 3.5
Divide both sides by 5:
$ r = \frac{3.5}{5} = 0.7 $
✔ r = 0.7
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19) 1500 – s = 1249
Subtract 1500 from both sides:
$ -s = 1249 - 1500 = -251 $
Multiply by -1:
$ s = 251 $
✔ s = 251
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20) ⅖ t = 12
Multiply both sides by 5:
$ \frac{2}{5}t = 12 \Rightarrow 2t = 60 $
Divide by 2:
$ t = 30 $
✔ t = 30
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✔ Final Answers:
| Question | Answer |
|--------|--------|
| 1) | a = 9 |
| 2) | b = 49 |
| 3) | c = 5 |
| 4) | d = 19 |
| 5) | e = 380 |
| 6) | f = 40 |
| 7) | g = 24 |
| 8) | h = 15 |
| 9) | i = 50 |
| 10) | j = 0.6 |
| 11) | k = 14 |
| 12) | l = 2.2 |
| 13) | m = 18 |
| 14) | n = 8.8 (or 8⅘) |
| 15) | o = 1.8 |
| 16) | p = 1.5 |
| 17) | q = 0.62 |
| 18) | r = 0.7 |
| 19) | s = 251 |
| 20) | t = 30 |
Let me know if you'd like this in printable format or with explanations for any specific steps!
Parent Tip: Review the logic above to help your child master the concept of 6th grade math equations worksheet.
