Here is the complete solution to all 18 problems from the worksheet “Expressions and Equations 6:1”, with clear explanations for each.
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1) What is the value of the expression 3a when a = 7?
- Substitute 7 for a:
→ 3 × 7 =
21
✔ Answer: 21
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2) Solve the equation 5b = 35.
- To solve for b, divide both sides by 5:
→ b = 35 ÷ 5 =
7
✔ Answer: b = 7
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3) Write the expression that matches the statement: 5 more than c.
- “More than” means addition. So, add 5 to c:
→
c + 5
✔ Answer: c + 5
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4) What is the value of the expression 2d − 3 when d = 11?
- Substitute 11 for d:
→ 2 × 11 − 3 = 22 − 3 =
19
✔ Answer: 19
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5) Solve the equation e − 12 = 19.
- Add 12 to both sides to isolate e:
→ e = 19 + 12 =
31
✔ Answer: e = 31
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6) Write the expression that matches the statement: multiply f by 3.
- “Multiply f by 3” means 3 times f:
→
3f
✔ Answer: 3f
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7) What is the value of the expression ½ g when g = 28?
- Substitute 28 for g:
→ ½ × 28 = 28 ÷ 2 =
14
✔ Answer: 14
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8) Solve the equation: h ÷ 3 = 12.
- Multiply both sides by 3 to isolate h:
→ h = 12 × 3 =
36
✔ Answer: h = 36
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9) Write the expression that matches the statement: subtract 8 from i.
- “Subtract 8 from i” means i minus 8:
→
i − 8
✔ Answer: i − 8
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10) What is the value of the expression: 100 − j when j = 76?
- Substitute 76 for j:
→ 100 − 76 =
24
✔ Answer: 24
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11) Solve the equation: 4k = 120.
- Divide both sides by 4:
→ k = 120 ÷ 4 =
30
✔ Answer: k = 30
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12) Write the expression that matches the statement: divide l by 3.
- “Divide l by 3” means l divided by 3:
→
l ÷ 3 or
l/3
✔ Answer: l ÷ 3 (or l/3)
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13) What is the value of the expression 2m + 3 when m = 4?
- Substitute 4 for m:
→ 2 × 4 + 3 = 8 + 3 =
11
✔ Answer: 11
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14) Solve the equation: 20 − n = 3.
- Subtract 20 from both sides:
→ −n = 3 − 20 = −17
Then multiply both sides by −1:
→ n =
17
✔ Answer: n = 17
*(Alternative method: Add n to both sides and subtract 3: 20 − 3 = n → n = 17)*
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15) Write the expression that matches the statement: double o and then add 1.
- “Double o” means 2 × o → 2o
- Then add 1 →
2o + 1
✔ Answer: 2o + 1
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16) What is the value of the expression: 3p − 5 when p = 6?
- Substitute 6 for p:
→ 3 × 6 − 5 = 18 − 5 =
13
✔ Answer: 13
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17) Solve the equation: ½ q = 10.
- Multiply both sides by 2 to eliminate the fraction:
→ q = 10 × 2 =
20
✔ Answer: q = 20
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18) Write the expression that matches the statement: subtract r from 15.
- “Subtract r from 15” means 15 minus r:
→
15 − r
✔ Answer: 15 − r
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✔ Final Answers Summary:
1) 21
2) b = 7
3) c + 5
4) 19
5) e = 31
6) 3f
7) 14
8) h = 36
9) i − 8
10) 24
11) k = 30
12) l ÷ 3 (or l/3)
13) 11
14) n = 17
15) 2o + 1
16) 13
17) q = 20
18) 15 − r
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Parent Tip: Review the logic above to help your child master the concept of 6th grade expressions and equations worksheet.
