Question

unit 4 lesson 4 cumulative practice problems 1. mia and tyler work on the equation (\frac{2}{5}b + 1 = -11) together. mias solution is (b = -25) and tyler says (b = -28). here is their work. do you agree with their solutions? explain or show your reasoning. mia: (\frac{2}{5}b + 1 = -11) (\frac{2}{5}b = -10) (b = -10 cdot \frac{5}{2}) (b = -25) tyler: (\frac{2}{5}b + 1 = -11) (2b + 1 = -55) (2b = -56) (b = -28)

Explanation:

Step1: Identify correct solving steps

Start with the original equation $\frac{2}{5}b + 1 = -13$

Step2: Isolate the variable term

Subtract 1 from both sides:
$\frac{2}{5}b = -13 - 1$
$\frac{2}{5}b = -14$

Step3: Solve for $b$

Multiply both sides by $\frac{5}{2}$:
$b = -14 \times \frac{5}{2}$
$b = -35$

Step4: Analyze Mia's error

Mia incorrectly calculated $-13 - 1$ as $-10$ instead of $-14$, then multiplied by $\frac{5}{2}$ incorrectly.

Step5: Analyze Tyler's error

Tyler incorrectly eliminated the fraction by multiplying only $\frac{2}{5}b$ by 5, not the entire left side. He should have calculated $5\times(\frac{2}{5}b + 1) = 5\times(-13)$, which gives $2b + 5 = -65$.

Answer:

I do not agree with either Mia's or Tyler's solutions. The correct value of $b$ is $-35$. Mia made an error when subtracting 1 from -13, and Tyler made a mistake when eliminating the fraction (he failed to multiply all terms on the left side by 5).