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Select the action you would use to solve [tex] \frac{x}{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]\(\frac{x}{3} = 12\)[/tex], we need to isolate the variable [tex]\(x\)[/tex]. Here is a step-by-step, detailed solution:

1. Identify the operation currently applied to [tex]\(x\)[/tex]:
- In the equation, [tex]\(x\)[/tex] is being divided by 3.

2. Determine the inverse operation:
- To undo the division by 3, we use multiplication by 3. This is because multiplication and division are inverse operations.

3. Perform the action to both sides of the equation:
- Multiply both sides by 3. This will cancel out the division by 3 on the left side of the equation, isolating [tex]\(x\)[/tex].
- So, the equation becomes:
[tex]\[ \frac{x}{3} \times 3 = 12 \times 3 \][/tex]
- This simplifies to:
[tex]\[ x = 36 \][/tex]

4. Justify the action using the appropriate property:
- The property that justifies multiplying both sides of the equation by 3 is the Multiplication 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.

Given these steps, the selections are:

- Action:
- B. Multiply both sides by 3.

- Property:
- E. Multiplication property of equality.

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