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Chapter 6: Problem 67

Solve each proportion and check. \(\frac{x-2}{12}=\frac{8}{3}\)

Short Answer

Expert verified
The solution to the given proportion is \(x = 34\)

Step by step solution

01

Cross-Multiplication

Perform cross-multiplication, implying that the product of the means equals the product of the extremes. This results in the equation: \((x - 2) * 3 = 12 * 8\). Simplify both sides of the equation to get: \(3x - 6 = 96\).
02

Simplify the Equation

Rearrange the equation to make \(x\) the subject by moving \(6\) to the other side. This results in: \(3x = 96 + 6\). Simplify further to get: \(3x = 102\).
03

Solve for \(x\)

Now solve for \(x\) by dividing both sides of the equation by \(3\). This gives: \(x = 102 / 3\). Simplify to get: \(x = 34\) as the solution.
04

Check Your Solution

Check the solution by substituting \(x = 34\) into the original proportion: \(\frac{34-2}{12} = \frac{8}{3}\). Simplify to see if both sides are equal: \(\frac{32}{12} = \frac{8}{3}\). After simplification both sides are not equal so the solution is correct because \(\frac{8}{3} = \frac{8}{3}\).

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