Let’s solve each problem one by one. We’ll use cross-multiplication for proportions — that means if you have:
> a/b = c/d
Then you can rewrite it as:
> a × d = b × c
Then solve the equation like normal algebra.
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Problem 1:
3/6 = (x - 3)/8
Cross multiply:
3 × 8 = 6 × (x - 3)
24 = 6(x - 3)
Divide both sides by 6:
4 = x - 3
Add 3 to both sides:
x = 7
✔ Check: Left side = 3/6 = 0.5; Right side = (7-3)/8 = 4/8 = 0.5 → Correct!
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Problem 2:
(x + 1)/(-4) = 2/3
Cross multiply:
3(x + 1) = -4 × 2
3(x + 1) = -8
Divide both sides by 3:
x + 1 = -8/3
Subtract 1:
x = -8/3 - 3/3 = -11/3
✔ Check: Left = (-11/3 + 1)/(-4) = (-8/3)/(-4) = (8/3)/4 = 8/12 = 2/3 → Correct!
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Problem 3:
(x + 2)/4 = 7/8
Cross multiply:
8(x + 2) = 4 × 7
8(x + 2) = 28
Divide by 8:
x + 2 = 28/8 = 7/2
Subtract 2:
x = 7/2 - 4/2 = 3/2
✔ Check: (3/2 + 2)/4 = (7/2)/4 = 7/8 → Correct!
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Problem 4:
7/11 = (x - 6)/5
Cross multiply:
7 × 5 = 11(x - 6)
35 = 11x - 66
Add 66:
101 = 11x
Divide by 11:
x = 101/11
✔ Check: (101/11 - 6)/5 = (101/11 - 66/11)/5 = (35/11)/5 = 35/55 = 7/11 → Correct!
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Problem 5:
8/6 = (x - 2)/6
Since denominators are same, numerators must be equal:
8 = x - 2
Add 2:
x = 10
✔ Check: (10 - 2)/6 = 8/6 → Correct!
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Problem 6:
5/(3 - x) = 7/10
Cross multiply:
5 × 10 = 7(3 - x)
50 = 21 - 7x
Subtract 21:
29 = -7x
Divide by -7:
x = -29/7
✔ Check: 5/(3 - (-29/7)) = 5/(3 + 29/7) = 5/(21/7 + 29/7) = 5/(50/7) = 5 × 7/50 = 35/50 = 7/10 → Correct!
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Problem 7:
(3 + x)/6 = 7/12
Cross multiply:
12(3 + x) = 6 × 7
12(3 + x) = 42
Divide by 12:
3 + x = 42/12 = 7/2
Subtract 3:
x = 7/2 - 6/2 = 1/2
✔ Check: (3 + 0.5)/6 = 3.5/6 = 7/12 → Correct!
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Problem 8:
3/5 = (x + 1)/9
Cross multiply:
3 × 9 = 5(x + 1)
27 = 5x + 5
Subtract 5:
22 = 5x
Divide by 5:
x = 22/5
✔ Check: (22/5 + 1)/9 = (27/5)/9 = 27/45 = 3/5 → Correct!
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Problem 9:
(x + 3)/5 = (6 + 4)/4 → Wait! That’s (x+3)/5 = 10/4? Let me check original.
Original says: (x + 3)/5 = (6 + 4)/4 → which is 10/4 = 5/2
So:
(x + 3)/5 = 5/2
Cross multiply:
2(x + 3) = 5 × 5
2(x + 3) = 25
Divide by 2:
x + 3 = 25/2
Subtract 3:
x = 25/2 - 6/2 = 19/2
✔ Check: (19/2 + 3)/5 = (25/2)/5 = 25/10 = 5/2 → and 10/4 = 5/2 → Correct!
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Problem 10:
(x + 7)/3 = 15/5 → 15/5 = 3
So:
(x + 7)/3 = 3
Multiply both sides by 3:
x + 7 = 9
Subtract 7:
x = 2
✔ Check: (2 + 7)/3 = 9/3 = 3 → and 15/5 = 3 → Correct!
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Problem 11:
3/5 = 6/(x + 3)
Cross multiply:
3(x + 3) = 5 × 6
3(x + 3) = 30
Divide by 3:
x + 3 = 10
Subtract 3:
x = 7
✔ Check: 6/(7 + 3) = 6/10 = 3/5 → Correct!
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Problem 12:
5/3 = (x - 2)/(-4)
Cross multiply:
5 × (-4) = 3(x - 2)
-20 = 3x - 6
Add 6:
-14 = 3x
Divide by 3:
x = -14/3
✔ Check: (-14/3 - 2)/(-4) = (-20/3)/(-4) = 20/12 = 5/3 → Correct!
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Final Answer:
1. x = 7
2. x = -11/3
3. x = 3/2
4. x = 101/11
5. x = 10
6. x = -29/7
7. x = 1/2
8. x = 22/5
9. x = 19/2
10. x = 2
11. x = 7
12. x = -14/3
Parent Tip: Review the logic above to help your child master the concept of solve proportion worksheet.
