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Select the action you would use to solve [tex]$x - 3 = 12$[/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: Subtract 3 from both sides.
D. Property: Addition property of equality.
E. Property: Multiplication property of equality.
F. Property: Subtraction property of equality.



Answer :

GinnyAnswer
To solve the equation [tex]\( x - 3 = 12 \)[/tex], we need to isolate the variable [tex]\( x \)[/tex]. Let's identify the appropriate action and the property that justifies it.

### Step-by-Step Solution

1. Identify the operation to isolate [tex]\( x \)[/tex]:
- The given equation is [tex]\( x - 3 = 12 \)[/tex].
- To isolate [tex]\( x \)[/tex], we need to get rid of the [tex]\(-3\)[/tex] that is subtracted from [tex]\(x\)[/tex]. The inverse operation of subtraction is addition.

2. Select the Action:
- To eliminate [tex]\(-3\)[/tex] from the left side, we add 3 to both sides of the equation.
- Thus, the action we would take is: Add 3 to both sides.

3. Apply the Action:
- Adding 3 to both sides of the equation:
[tex]\[ x - 3 + 3 = 12 + 3 \][/tex]
- Simplifies to:
[tex]\[ x = 15 \][/tex]

4. Justify the Action with a Property:
- The Addition Property of Equality states that if you add the same number to both sides of an equation, the equality is still maintained.
- Therefore, the property that justifies our action is: Addition Property of Equality.

### Conclusion

Based on the steps above,
- Action: Add 3 to both sides (Option A).
- Property: Addition Property of Equality (Option D).

Thus, the correct selections are:
- A. Action: Add 3 to both sides
- D. Property: Addition property of equality

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