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Chapter 6: Problem 69

Solve each proportion and check. \(\frac{x}{7}=\frac{x+14}{5}\)

Short Answer

Expert verified
The solution to the proportion is \(x = -49\).

Step by step solution

01

Cross Multiply

Cross multiply to eliminate the fractions and get: \(5x = 7(x + 14)\)
02

Simplify

Expand the right-hand side of the equation to get: \(5x = 7x + 98\)
03

Solve for x

Subtract \(7x\) from both sides of the equation to solve for \(x\), getting: \(-2x = 98\) and then divide both sides by -2 to isolate \(x\) and solve: \(x = -49\)
04

Verify the solution

Substitute \(x = -49\) into the original equation to verify the solution: \(-49/7 = -49+14/5 \Rightarrow -7 = -7\). Both sides of the equation are equal, confirming that the solution is correct.

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