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Chapter 6: Problem 70

Solve each proportion and check. \(\frac{x}{5}=\frac{x-3}{2}\)

Short Answer

Expert verified
The solution to the given proportion is x = 5.

Step by step solution

01

Cross-Multiplication

Start by multiplying each side of the equation by the denominator of the other side. This will give \((x)(2) = (5)(x-3)\).
02

Simplify

Simplify to get \(2x = 5x - 15\).
03

Rearrange the equation

Rearrange the equation to isolate the variable \(x\) on one side. To do this, subtract \(2x\) from both sides, resulting in \(5x - 2x = 15\). Simplify it further to get \(3x = 15\).
04

Solve for x

Solve for \(x\) by dividing by 3 on both sides. This yields \(x = 5\).
05

Check the solution

Substitute \(x = 5\) back into the original fraction to confirm whether it maintains the proportion. If \(\frac{5}{5} = \frac{2}{2}\), then the solution is correct.

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