Problem 40
Question
SOLVING EQUATIONS Multiply by a reciprocal to solve the equation. $$ 12=\frac{2}{3} x $$
Step-by-Step Solution
Verified Answer
The solution to the equation \(12=\frac{2}{3} x\) is \(x = 18\).
1Step 1: Understand the Problem
The equation to solve is \(12=\frac{2}{3} x\). The goal is to isolate \(x\) on one side of the equation for which you need to deal with the fraction.
2Step 2: Multiply by Reciprocal
To get rid of the fraction, multiply both sides by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\). That gives you: \(12 * \frac{3}{2} = x * \frac{2}{3} * \frac{3}{2}\)
3Step 3: Simplify the Equation
After multiplying, simplify the equation. The \(2\)s cancel in the right side of the equation and the numbers multiply in the left side of the equation. This leaves you with: \(18 = x\)
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