Problem 95 - Introductory Algebra for College Students

Question

Determine whether the given number is a solution of the equation. $$20-\frac{1}{3} z=\frac{1}{2} z ; 12$$

Step-by-Step Solution

Answer

The provided number, 12, is not a solution to the equation.

Step 1: Substitute the given number for z in the equation

Put 12 in place of \(z\) in the equation: \(20-\frac{1}{3}*(12) = \frac{1}{2}*12\).

Step 2: Simplify the equation

On the left side of the equation, we need to multiply \(-\frac{1}{3}\) and 12. As multiplication comes before subtraction in the order of operations, we do this first. This gives us: \(20 - 4 = 6\). The right side simplifies to 6.

Step 3: Check if both sides of the equation are equal

After simplification, both sides of the equation become 16 = 6, which is not true. Therefore, the number 12 is not a solution to the equation.