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Chapter 1: Problem 91

Determine whether the given number is a solution of the equation. $$\frac{7}{2} x=28 ; 8$$

Short Answer

Expert verified
Yes, the given number 8, is the solution to the equation \(\frac{7}{2} x=28\).

Step by step solution

01

Evaluating the given equation

The equation presented in the exercise is \( \frac{7}{2} x=28 \). The goal is to isolate x on one side of the equation.
02

Solve for x

To solve for x, divide both sides of the equation by \(\frac{7}{2}\) (or multiply both sides by \(\frac{2}{7}\)). Doing this gives the result: \(x = 28 \div \frac{7}{2} = 28 \times \frac{2}{7} = 8\). This means if \(x = 8\), the equation is true.
03

Comparing the result with the given number

The given number to check is also 8. Since the result for x and the given number match, it can be concluded that the given number is indeed a solution to the equation.

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