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Select the action you would use to solve [tex]\(\frac{z}{3} = 12\)[/tex]. Then select the property that justifies that action.

Select all that apply:

A. Action: Add 3 to both sides.

B. Action: Multiply both sides by 3.

C. Action: Divide both sides by 3.

D. Property: Addition property of equality.

E. Property: Multiplication property of equality.

F. Property: Division property of equality.



Answer :

GinnyAnswer
To solve the equation [tex]\(\frac{z}{3} = 12\)[/tex], we want to isolate the variable [tex]\(z\)[/tex]. Here is a step-by-step solution:

1. Action: To isolate [tex]\(z\)[/tex], we need to eliminate the denominator in the fraction [tex]\(\frac{z}{3}\)[/tex].
- The most effective way to do that is by multiplying both sides of the equation by 3.
- Hence, the selected action is: B. Action: Multiply both sides by 3.

2. Property: The justification for multiplying both sides of the equation by the same number is based on a fundamental property of equality.
- This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.
- Therefore, the property that justifies this action is: E. Property: Multiplication property of equality.

So, the correct selections are:
- Action: B. Action: Multiply both sides by 3.
- Property: E. Property: Multiplication property of equality.

Thus, the solution steps highlight:
- Multiplying both sides by 3 to isolate [tex]\(z\)[/tex].
- Justifying this action using the multiplication property of equality.

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