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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.

Sagot :

GinnyAnsweridn
To solve the equation [tex]\(\frac{x}{3} = 12\)[/tex], we need to isolate [tex]\(x\)[/tex]. Let's break down the process step-by-step:

1. Identify the equation and the goal:
- The equation is [tex]\(\frac{x}{3} = 12\)[/tex].
- The goal is to solve for [tex]\(x\)[/tex].

2. Determine the action needed to isolate [tex]\(x\)[/tex]:
- Since [tex]\(x\)[/tex] is divided by 3, we can eliminate the division by multiplying both sides of the equation by 3. This is because multiplication is the inverse operation of division.

3. Perform the action:
- Multiply both sides of the equation by 3:
[tex]\[ 3 \cdot \frac{x}{3} = 3 \cdot 12 \][/tex]
- Simplify the equation:
[tex]\[ x = 36 \][/tex]

4. State the actions and properties that justify the solution:
- The action used is: Multiply both sides by 3.
- The property that justifies this action is: Multiplication property of equality, which states that both sides of an equation remain equal if they are multiplied by the same number.

Therefore, the correct selections are:
- Action: B. Multiply both sides by 3.
- Property: E. Multiplication property of equality.
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