Question

2
select the correct answer.
what is the justification for step 4 in the solution process?
\\( \frac{9}{2}b + 11 - \frac{5}{6}b = b + 2 \\)
step 1 : \\( \frac{22}{6}b + 11 = b + 2 \\)
step 2 : \\( \frac{8}{3}b + 11 = 2 \\)
step 3 : \\( \frac{8}{3}b = -9 \\)
step 4 : \\( b = -\frac{27}{8} \\)
\\( \bigcirc \\) a. the addition property of equality
\\( \bigcirc \\) b. combining like terms
\\( \bigcirc \\) c. the subtraction property of equality
\\( \bigcirc \\) d. the multiplication property of equality
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Explanation:

To determine the justification for Step 4, we analyze the transition from Step 3 ($\frac{8}{3}b = -9$) to Step 4 ($b = -\frac{27}{8}$). The multiplication property of equality states that if we multiply both sides of an equation by the same non - zero number, the equation remains true. In Step 4, we multiply both sides of $\frac{8}{3}b=-9$ by the reciprocal of $\frac{8}{3}$, which is $\frac{3}{8}$. So, $b=-9\times\frac{3}{8}=-\frac{27}{8}$. This operation is justified by the multiplication property of equality.

• Option A (addition property of equality) is incorrect because we are not adding a number to both sides.
• Option B (combining like terms) is incorrect as there are no like terms to combine in this step.
• Option C (subtraction property of equality) is incorrect as we are not subtracting a number from both sides.

Answer:

D. the multiplication property of equality