Problem 93 - Introductory Algebra for College Students

Question

Determine whether the given number is a solution of the equation. $$w-\frac{2}{3}=\frac{3}{4} ; 1 \frac{5}{12}$$

Step-by-Step Solution

Answer

Yes, 1 5/12 is a solution to the given equation.

Step1: Convert the Mixed Number

Convert the given mixed number 1 5/12 into an improper fraction or decimal number. An improper fraction is created by multiplying the denominator by the whole number and then adding the numerator. Here, (12*1) + 5 = 17, so the improper fraction is 17/12.

Step 2: Substitute into the Equation

Now substitute the improper fraction for the variable 'w' in the equation. Therefore, the equation becomes 17/12 - 2/3 = 3/4. In order to perform the subtraction, first convert all fractions to have the common denominator, which is 12 in our case.

Step 3: Simplify the Equation

After converting into fractions with common denominator, the equation becomes 17/12 - 8/12 = 9/12. By simplifying the left side, we get 9/12 = 9/12.

Step 4: Verifying the Equality

The left and right sides are now both equal to 9/12, so the equation is balanced. Therefore, the given mixed number is indeed a solution to the equation.