Question

select the correct answer.
victor solved this inequality as shown:
step 1: 3x - 5 > x + 5
step 2: 2x - 5 > 5
step 3: 2x > 10
step 4: x > 5
what property justifies the work between step 3 and step 4?
a. division property of inequality
b. inverse property of multiplication
c. subtraction property of inequality
d. transitive property of inequality

Explanation:

To determine the property justifying the work between Step 3 ($2x > 10$) and Step 4 ($x > 5$), we analyze each option:

• Option A: The division property of inequality states that if we divide both sides of an inequality by a positive number, the inequality sign remains the same. Here, we divide both sides of $2x > 10$ by 2 (a positive number) to get $x > 5$, which matches this property.
• Option B: The inverse property of multiplication involves multiplying a number by its reciprocal to get 1, which is not relevant here.
• Option C: The subtraction property of inequality involves subtracting a number from both sides, but we are dividing here, so this is incorrect.
• Option D: The transitive property of inequality deals with relationships between three quantities (if $a > b$ and $b > c$, then $a > c$), which is not applicable here.

Answer:

A. division property of inequality