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.
