Chapter 8.1, Problem 51HP

To determine

Whether the equation $3x=15$ can be solved using the Multiplication Property of Equality.

Answer to Problem 51HP

  $\text{Yes, it can be solved by multiplying both sides by }\frac{1}{3}$

Explanation of Solution

Given:

The equation, $3x=15$

Concept used:

• The distributive property of binomials (FOIL): $\left(a+b\right)\left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d$
• Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

Yes, the given equation can be solved using the Multiplication Property of Equality. In order to solve the given equation using the Multiplication Property of Equality, one can multiply both sides by

  $\frac{1}{3}$ and can simplify further as shown below

  $\begin{array}{c}3x=15\\ 3x\cdot \frac{1}{3}=15\cdot \frac{1}{3}\\ \frac{3x}{3}=\frac{15}{3}\\ x=5\end{array}$

Thus, the given equation can be solved using the Multiplication Property of Equality.