Question

question 3 of 10
select the action you would use to solve ( x - 3 = 12 ). 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

Explanation:

To solve the equation \( x - 3 = 12 \), we want to isolate \( x \). The term with \( x \) is \( x - 3 \), so we need to get rid of the \(-3\). By adding 3 to both sides, we can cancel out the \(-3\) on the left. This action is justified by the addition property of equality, which states that if we add the same number to both sides of an equation, the equation remains true.

• Option A: Adding 3 to both sides (\( (x - 3)+3 = 12 + 3 \)) simplifies to \( x=15 \), which isolates \( x \), so this action is correct.
• Option B: Multiplying both sides by 3 would give \( 3(x - 3)=36 \) or \( 3x - 9 = 36 \), which does not isolate \( x \) directly, so this is incorrect.
• Option C: Subtracting 3 from both sides would give \( x - 6 = 9 \), which moves us further from isolating \( x \), so this is incorrect.
• Option D: The addition property of equality allows us to add the same number to both sides, which is what we did (adding 3), so this property is correct.
• Option E: The multiplication property of equality is for multiplying both sides by a number, which we didn't do, so this is incorrect.
• Option F: The subtraction property of equality is for subtracting the same number from both sides, which we didn't do (we added), so this is incorrect.

Answer:

A. Action: Add 3 to both sides.
D. Property: Addition property of equality