Problem 91 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.

Step 3: 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.