Question

practice problems
1 mai and tyler work on the equation \\(\frac{2}{5}b + 1 = -11\\) together. mais solutio
tylers is \\(b = -28\\). here is their work. do you agree with their solutions?
your reasoning.
mai:
\\(\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\\)

2 solve \\(3(x - 4) = 12x\\)

3 next to each arrow, describe what is done in each step.
\\(2(-3x + 4) = 5x + 2\\)
\\(-6x + 8 = 5x + 2\\)
\\(8 = 11x + 2\\)

Explanation:

Problem 1: Analyze Mai and Tyler's Solutions

Step 1: Solve the equation $\frac{2}{5}b + 1 = -11$ correctly

Subtract 1 from both sides: $\frac{2}{5}b = -11 - 1 = -12$
Multiply both sides by $\frac{5}{2}$: $b = -12 \times \frac{5}{2} = -30$

Step 2: Check Mai's work

Mai subtracted 1 incorrectly: $\frac{2}{5}b = -10$ (should be -12). So her solution $b = -25$ is wrong.

Step 3: Check Tyler's work

Tyler multiplied by 5 incorrectly: $2b + 5 = -55$ (he did $2b + 1 = -55$). So his solution $b = -28$ is wrong.

Step 1: Distribute the left side

$3x - 12 = 12x$

Step 2: Subtract $3x$ from both sides

$-12 = 9x$

Step 3: Divide by 9

$x = \frac{-12}{9} = -\frac{4}{3}$

1. First arrow (left): Distribute 2 to $-3x$ and 4: $2(-3x) + 2(4) = -6x + 8$, so the step is Distribute 2.
2. Second arrow (right): Add $6x$ to both sides: $-6x + 8 + 6x = 5x + 2 + 6x \implies 8 = 11x + 2$, so the step is Add $6x$ to both sides.

Answer:

Neither Mai's ($b = -25$) nor Tyler's ($b = -28$) solution is correct. The correct solution is $b = -30$.

Problem 2: Solve $3(x - 4) = 12x$