To solve the equation [tex]\(\frac{x}{3} = 12\)[/tex], we need to isolate [tex]\(x\)[/tex]. Here are the steps to solve this equation and the justification for each action taken:
1. Identify the current state of the variable [tex]\(x\)[/tex]:
The equation [tex]\(\frac{x}{3} = 12\)[/tex] tells us that [tex]\(x\)[/tex] divided by 3 equals 12.
2. Determine the action needed to isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to get rid of the division by 3. To do this, we need to do the opposite operation of division, which is multiplication.
3. Apply the action to both sides of the equation:
Multiply both sides of the equation by 3 to cancel out the division by 3 on the left side.
[tex]\[
\left(\frac{x}{3}\right) \times 3 = 12 \times 3
\][/tex]
Simplifying both sides:
[tex]\[
x = 36
\][/tex]
4. Justify the action using the appropriate property:
The action of multiplying both sides of the equation by 3 is justified by the Multiplication Property of Equality. This property states that if you multiply both sides of an equation by the same nonzero number, the two sides remain equal.
Based on these steps, the correct choices are:
- Action: Multiply both sides by 3 (Choice B)
- Property: Multiplication property of equality (Choice E)
Therefore, the correct responses are:
- B. Action: Multiply both sides by 3
- E. Property: Multiplication property of equality
