Problem 94 - Introductory Algebra for College Students

Question

Determine whether the given number is a solution of the equation. $$w-\frac{3}{4}=\frac{7}{4} ; 2 \frac{1}{2}$$

Step-by-Step Solution

Answer

Yes, the given number \(2 \frac{1}{2}\) is indeed a solution of the given equation.

Step 1: Identify The Equation And The Given Number

The given equation is \(w-\frac{3}{4}=\frac{7}{4}\). And the given number which might be a solution of the equation is \(2 \frac{1}{2}.\)

Step 2: Substitute The Number Into The Equation

Substitute the number \(2 \frac{1}{2}\) for \( w \) into the equation: \(2 \frac{1}{2} - \frac{3}{4} = \frac{7}{4}\). To make the calculations easier, convert the mixed number \(2 \frac{1}{2}\) to an improper fraction. So, \( w = \frac{5}{2}\) and the equation becomes: \( \frac{5}{2} - \frac{3}{4} = \frac{7}{4}\)

Step 3: Solve The Equation

Solve the equation on the left-hand side. To subtract the fractions, they need to have the same denominator. So, convert \(\frac{5}{2}\) into quarters, which equals \( \frac{10}{4} \). Now, subtract \( \frac{3}{4} \) from \( \frac{10}{4} \), which results in \( \frac{7}{4} \).

Step 4: Compare Both Sides

Now, the left-hand side of equation equals to the right-hand side, which means \(2 \frac{1}{2}\) is a solution of the given equation.