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Leon tried to solve an equation step by step.

{:[(1)/(2)w-12=18],[(1)/(2)w=30quad" Step 1 "],[w=15quad" Step 2 "]:}
Find Leon's mistake.
Choose 1 answer:
(A) Step 1
(B) Step 2
(c) Leon did not make a mistake.

Leon tried to solve an equation step by step. $\newline$ $\begin{aligned} \frac{1}{2} w-12 & =18 \\ \frac{1}{2} w & =30 \quad \text { Step } 1 \\ w & =15 \quad \text { Step 2 } \end{aligned}$ $\newline$ Find Leon's mistake. $\newline$ Choose $1$ answer: $\newline$ (A) $\operatorname{Step} 1$ $\newline$ (B) Step $2$ $\newline$ (C) Leon did not make a mistake.

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Solve a system of equations using any method: word problems

Full solution

Q. Leon tried to solve an equation step by step.

\newline

\begin{aligned} \frac{1}{2} w-12 & =18 \\ \frac{1}{2} w & =30 \quad \text { Step } 1 \\ w & =15 \quad \text { Step 2 } \end{aligned}

\newline

Find Leon's mistake.

\newline

Choose

1

answer:

\newline

(A)

\operatorname{Step} 1

\newline

(B) Step

2

\newline

(C) Leon did not make a mistake.

Start with equation: Leon starts with the equation $\frac{1}{2}w - 12 = 18$ . $\newline$ To isolate $w$ , he adds $12$ to both sides of the equation. $\newline$ $\frac{1}{2}w - 12 + 12 = 18 + 12$ $\newline$ $\frac{1}{2}w = 30$ $\newline$ He labels this as ＂Step $1$ ＂.
Isolate variable: In ＂Step $2$ ＂, Leon multiplies both sides of the equation by $2$ to solve for $w$ . $\newline$ $2 \cdot \frac{1}{2}w = 2 \cdot 30$ $\newline$ $w = 60$ $\newline$ However, Leon writes $w = 15$ , which is incorrect.

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