To determine which property justifies the transition from Step 3 to Step 4 in Victor's solution of the inequality, let's carefully examine the steps provided:
- Step 1: [tex]\( 3x - 5 > x + 5 \)[/tex]
- Step 2: [tex]\( 2x - 5 > 5 \)[/tex]
(This is obtained by subtracting [tex]\( x \)[/tex] from both sides of the inequality)
- Step 3: [tex]\( 2x > 10 \)[/tex]
(This is obtained by adding 5 to both sides of the inequality)
- Step 4: [tex]\( x > 5 \)[/tex]
(Here, Victor divided both sides of the inequality by 2)
When we look specifically at the change from Step 3 ([tex]\( 2x > 10 \)[/tex]) to Step 4 ([tex]\( x > 5 \)[/tex]), we see the operation performed is dividing each side of the inequality by 2.
When you divide both sides of an inequality by a positive number, the direction of the inequality remains unchanged. This is known as the division property of inequality.
Thus, the property that justifies the work between Step 3 and Step 4 is:
A. division property of inequality
