Question

taylors work solving an equation is shown here. do you agree with her work and her final answer? taylors work 5(b + 2)=2(3 - b)+6b 5b + 10=2(3 - b)+6b 5b + 10=6 - 2b+6b 5b + 10=6+4b -4b -4b b + 10=6 -10 -10 b=-4 taylor made a mistake when solving. she should have subtracted 5b from both sides instead of 4b. taylor made a mistake when combining like terms. 2b + 6b makes 8b, not 4b. i agree with taylors final answer, but she could have been more efficient if she did all of the distribution at the same time. taylor made a mistake when distributing on the right. she should have gotten 6 - b + 6b instead of 6 - 2b + 6b.

Explanation:

Step1: Analyze Taylor's distribution

Starting with $5(b + 2)=2(3 - b)+6b$. Distributing on the left - hand side gives $5b+10$, and on the right - hand side, $2(3 - b)=6 - 2b$, so $5b + 10=6 - 2b+6b$ is correct.

Step2: Analyze Taylor's combining like - terms

Combining like - terms on the right - hand side, $-2b+6b = 4b$, so $5b + 10=6 + 4b$ is correct.

Step3: Analyze Taylor's isolation of variable

Subtracting $4b$ from both sides gives $b + 10=6$, and then subtracting 10 from both sides gives $b=-4$, which is correct. But distributing all at once could be more efficient. For example, starting with $5(b + 2)=2(3 - b)+6b$, we have $5b+10 = 6-2b + 6b$, and we could also expand it as $5b+10=6 + 4b$, and then solve for $b$.

Answer:

I agree with Taylor's final answer, but she could have been more efficient if she did all of the distribution at the same time.