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Learn how to solve multi-step proportions easily with a couple of good examples.
Quick review:
Suppose you have the following proportion:
Numerator #1 / Denominator #1 = Numerator #2 / Denominator #2
After doing cross-multiplication, it is equivalent to
Numerator #1 × Denominator #2 = Numerator #2 × Denominator #1
Example #1
Solve the proportion (x - 5) / 4 = (x + 3) / 6
(x - 5) / 4 = (x + 3) / 6
The proportion is equivalent to
(x - 5) × 6 = (x + 3) × 4
(x - 5) × 6 = (x + 3) × 4
Use the distributive property
6x - 30 = 4x + 12
Subtract 4x from each side of the equation
6x - 4x - 30 = 4x - 4x + 12
2x - 30 = 0 + 12
2x - 30 = 12
Add 30 to each side of the equation
2x - 30 + 30 = 12 + 30
2x + 0 = 42
2x = 42
Divide each side by 2
2x/2 = 42/2
x = 21
Example #2
Solve the proportion 3 / (x - 4) = -5 / (4x + 1)
3 / (x - 4) = -5 / (4x + 1)
The proportion is equivalent to
3 × (4x + 1) = -5 × (x - 4)
3 × (4x + 1) = -5 × (x - 4)
Use the distributive property
12x + 3 = -5x + 20
Add 5x to each side of the equation
12x + 5x + 3 = -5x + 5x + 20
17x + 3 = 0 + 20
17x + 3 = 20
Subtract 3 from each side of the equation
17x + 3 - 3 = 20 - 3
17x + 0 = 17
17x = 17
Divide each side by 17
17x/17 = 17/17
x = 1
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