Problem 96 - Introductory Algebra for College Students

Question

Determine whether the given number is a solution of the equation. $$12-\frac{1}{4} z=\frac{1}{2} z ; 20$$

Step-by-Step Solution

Answer

The number 20 is not a solution to the given equation.

Step 1: Identify The Provided Value and Equation

In this problem, we are provided with the equation \(12-\frac{1}{4} z=\frac{1}{2} z\) and the number 20 which is proposed as a potential solution for \(z\).

Step 2: Substitute The Provided Number Into The Equation

We substitute \(z = 20\) into the equation. This gives us \(12-\frac{1}{4} * 20 = \frac{1}{2}*20\).

Step 3: Simplify Both Sides Of The Equation

When we simplify the left hand side, we get \(12 - 5 = 7\). And when we simplify the right hand side, we get \(\frac{1}{2} * 20 = 10\).

Step 4: Compare Both Sides Of The Equation

After substituting the value of z into the equation and simplifying, we see that the values are not equal. The left hand side equals 7 and the right hand side equals 10.