Sure, let's go through the steps to understand the justification for Step 2 in the given equation:
Given:
[tex]\[ 10x - 25 - 3x = 4x - 1 \][/tex]
Step 1: Combine like terms on the left side.
[tex]\[ (10x - 3x) - 25 = 4x - 1 \][/tex]
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
Step 2: Isolate the variable terms on one side and constants on the other side.
To do this, we need to move [tex]\(-25\)[/tex] from the left side to the right side by adding 25 to both sides of the equation:
[tex]\[ 7x - 25 + 25 = 4x - 1 + 25 \][/tex]
[tex]\[ 7x = 4x + 24 \][/tex]
The justification for Step 2 involves adding 25 to both sides of the equation to isolate the variable terms, which follows the principle of:
B. the subtraction property of equality.
The subtraction property of equality states that if you add or subtract the same number on both sides of an equation, the equality is maintained. In this case, adding 25 to both sides effectively cancelled out the [tex]\(-25\)[/tex] on the left side, isolating the variable terms.
