To identify which property is illustrated in step 8, let's review the steps leading to and including step 8:
Step 1: [tex]\( 2(x+4)-4x=1+x \)[/tex]
Step 2: [tex]\( 2x + 8 - 4x = 1 + x \)[/tex]
Step 3: [tex]\( 8 - 2x = 1 + x \)[/tex]
Step 4: [tex]\( 8 - 2x - x = 1 + x - x \)[/tex]
Step 5: [tex]\( 8 - 3x = 1 \)[/tex]
Step 6: [tex]\( 8 - 3x - 8 = 1 - 8 \)[/tex]
Step 7: [tex]\( -3x = -7 \)[/tex]
Step 8: [tex]\( x = \frac{7}{3} \)[/tex]
In step 8, we solve for [tex]\( x \)[/tex] by dividing both sides of the equation [tex]\( -3x = -7 \)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[ x = \frac{7}{3} \][/tex]
This illustrates the Division property of equality, which states that if you divide both sides of an equation by the same nonzero number, the equality is preserved.
Thus, the correct answer is:
D. Division property of equality
