Answer :
Let's solve the given algebraic equation and identify the justification for each step.
Given equation:
[tex]\[10x - 25 - 3x = 4x - 1\][/tex]
Step 1: Simplify the left side of the equation by combining like terms:
[tex]\[ (10x - 3x) - 25 = 4x - 1 \][/tex]
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
So, at the end of Step 1, we have:
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
Step 2: To isolate the variable term on one side of the equation, we need to add 25 to both sides:
[tex]\[ 7x - 25 + 25 = 4x - 1 + 25 \][/tex]
[tex]\[ 7x = 4x + 24 \][/tex]
This step is justified by the addition property of equality, which states that adding the same number to both sides of an equation keeps the equation balanced.
Therefore, the correct answer is:
[tex]\[ B. \text{the addition property of equality} \][/tex]
Given equation:
[tex]\[10x - 25 - 3x = 4x - 1\][/tex]
Step 1: Simplify the left side of the equation by combining like terms:
[tex]\[ (10x - 3x) - 25 = 4x - 1 \][/tex]
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
So, at the end of Step 1, we have:
[tex]\[ 7x - 25 = 4x - 1 \][/tex]
Step 2: To isolate the variable term on one side of the equation, we need to add 25 to both sides:
[tex]\[ 7x - 25 + 25 = 4x - 1 + 25 \][/tex]
[tex]\[ 7x = 4x + 24 \][/tex]
This step is justified by the addition property of equality, which states that adding the same number to both sides of an equation keeps the equation balanced.
Therefore, the correct answer is:
[tex]\[ B. \text{the addition property of equality} \][/tex]
