Question

What property of equality of congruence is this?

“If x/5=30, then x=150”

A. Addition property
B. Subtraction property
C. Multiplication property
D. Division property
C. Partition property
D. Reflexive property
E. Transitive property
F. Substitution property

Answer 1

C. Multiplication property

Explanation:

Properties of equality and congruence are properties that show how equations or shapes can be changed but remain equal.

Properties of Equality

Since this question deals with an equation, not a shape, the properties of equality will be used. The most common properties of equality include:

• Addition - states that if the same number is added to both sides, the equation is still equal.
• Subtraction - states that if the same number is subtracted from both sides, the equation remains true.
• Multiplication - states that if the same number is multiplied on both sides, the equation is still true.
• Division - states that if the same number is divided on both sides, the equation remains equal.

The important thing to note is that whatever is done to one side, must be done to both. No matter what operation it is, if you change the equation you must change both sides equally.

Solving for X

To find the correct property, we need to solve for x. Do this by isolating the variable.

First, let's rewrite the equation.

• 
  `\displaystyle(x)/(5)=30`

Now, we need to find a way to isolate the variable. To isolate x, we need to get rid of the denominator, 5. Do this by multiplying both sides by 5. This will cancel out the denominator on the left side. Remember to multiply on both sides.

• 
  `\displaystyle(x)/(5)*5 =30*5`

Then, simplify the equation

• 
  `x=150`

To solve this equation, we multiplied both sides by the same number. This matches the definition of the multiplication property of equality, so that must be the correct answer.