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Select the action you would use to solve [tex]3x = 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]\(3x = 12\)[/tex], we need to isolate [tex]\(x\)[/tex] on one side of the equation. Here is a detailed step-by-step solution:

1. Identify the equation to solve:
[tex]\[3x = 12\][/tex]

2. Determine the action needed to isolate [tex]\(x\)[/tex]:
- We need to get [tex]\(x\)[/tex] by itself on one side of the equation. Currently, [tex]\(x\)[/tex] is multiplied by 3.
- To isolate [tex]\(x\)[/tex], we should perform the inverse operation of multiplication, which is division.

3. Select the appropriate action:
- Action: Divide both sides by 3.

This is because we want to undo the multiplication of [tex]\(x\)[/tex] by 3.

4. Apply the division to both sides:
[tex]\[ \frac{3x}{3} = \frac{12}{3} \][/tex]

5. Simplify:
[tex]\[ x = 4 \][/tex]

6. Identify the property that justifies this action:
- The Division property of equality states that if you divide both sides of an equality by the same non-zero number, the two sides remain equal.

Thus, the appropriate choices are:

- C. Action: Divide both sides by 3.
- F. Property: Division property of equality.

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