Find solutions to your questions with the help of IDNLearn.com's expert community. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

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


Sagot :

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.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.