Let's solve the equation step by step:
The given equation is:
[tex]\[ 12 - x = 7x + 32 \][/tex]
Step 1: Move all terms involving [tex]\( x \)[/tex] to one side of the equation and constant terms to the other side.
[tex]\[ 12 - x - 7x = 7x + 32 - 7x \][/tex]
[tex]\[ 12 - 8x = 32 \][/tex]
Step 2: Simplify the equation from Step 1 to isolate [tex]\( x \)[/tex].
[tex]\[ -8x = 32 - 12 \][/tex]
[tex]\[ -8x = 20 \][/tex]
The justification for isolating the [tex]\( x \)[/tex] term involves rearranging the equation by subtracting [tex]\( 12 \)[/tex] from both sides, which leads us to:
[tex]\[ -8x = 20 \][/tex]
Therefore, the correct justification corresponds to the subtraction property of equality because we are subtracting the same amount (12) from both sides of the equation.
B. the subtraction property of equality
