The first and second steps to solve the equation $\frac{3 x}{5}+5=20$ are shown below.
$\begin{array}{l}
\frac{3 x}{5}+5-5=20-5 \\
\frac{3 x}{5}\left(\frac{5}{3}\right)=15\left(\frac{5}{3}\right)
\end{array}$
Which property was applied in the second step?
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Multiplication Property of Equality
D. Division Property of Equality
Answer (1)
The second step involves multiplying both sides of the equation by the same value, which is the Multiplication Property of Equality. Therefore, the answer is Multiplication Property of Equality.
Explanation
Understanding the Problem We are given the equation 5 3 x + 5 = 20 and the first two steps of its solution. We need to identify the property of equality that justifies the second step.
Analyzing the First Step The first step is 5 3 x + 5 − 5 = 20 − 5 , which simplifies to 5 3 x = 15 . This step uses the Subtraction Property of Equality.
Identifying the Property Used in the Second Step The second step is 5 3 x ( 3 5 ) = 15 ( 3 5 ) . Here, both sides of the equation 5 3 x = 15 are multiplied by 3 5 . This is an application of the Multiplication Property of Equality.
Stating the Multiplication Property of Equality The Multiplication Property of Equality states that if you multiply both sides of an equation by the same non-zero number, the equation remains balanced.
Conclusion Therefore, the property applied in the second step is the Multiplication Property of Equality.
Examples
Imagine you're baking a cake and the recipe calls for balancing ingredients. If you double the amount of flour, you must also double the amount of sugar to keep the cake tasting right. This is similar to the Multiplication Property of Equality: whatever you do to one side of the equation (or recipe), you must do to the other to maintain balance and equality. This principle is crucial not only in baking but also in various real-life scenarios, such as adjusting quantities in recipes, scaling measurements in construction, or modifying budgets proportionally.
