Answered

What error did Malik make first when solving the equation [tex]\(\frac{2}{5} x - 4 y = 10\)[/tex]?

Given solution:
[tex]\[
\begin{array}{l}
\frac{2}{5} x - 4 y = 10 \\
\frac{2}{5} x - 4(60) = 10 \\
\frac{2}{5} x - 240 = 10 \\
\frac{2}{5} x - 240 + 240 = 10 + 240 \\
\frac{5}{2}\left(\frac{2}{5} x\right) = \frac{5}{2}(250) \\
x = 265
\end{array}
\][/tex]

A. Malik did not multiply [tex]\(\frac{5}{2}(250)\)[/tex] correctly.
B. Malik added 240 to each side of the equation.
C. Malik did not multiply [tex]\(\frac{5}{2}\left(\frac{2}{5} x\right)\)[/tex] correctly.
D. Malik substituted 60 for [tex]\(y\)[/tex] instead of [tex]\(x\)[/tex].



Answer :

To determine the error Malik made, let's carefully consider each step presented and recognize where the mistake occurred.

Given the equation:
[tex]\[ \frac{2}{5} x - 4 y = 10 \][/tex]

The steps are as follows:

1. Substitute a value (substitution step).
2. Simplify the equation by performing operations (arithmetic steps).
3. Isolate the variable and solve it (solving step).

Malik's work is shown as:
[tex]\[ \frac{2}{5} x - 4 y = 10 \][/tex]
[tex]\[ \frac{2}{5} x - 4(60) = 10 \][/tex]
[tex]\[ \frac{2}{5} x - 240 = 10 \][/tex]
[tex]\[ \frac{2}{5} x - 240 + 240 = 10 + 240 \][/tex]
[tex]\[ \frac{5}{2} \left[\frac{2}{5} x\right] = \frac{5}{2} [250] \][/tex]
[tex]\[ x = 265 \][/tex]

Let's analyze the first main step where Malik substituted the value 60. The initial equation is [tex]\(\frac{2}{5} x - 4 y = 10\)[/tex]. In Malik's solution, the substitution was made:
[tex]\[ \frac{2}{5} x - 4(60) = 10 \][/tex]

Here, 60 was substituted for [tex]\(y\)[/tex]. Since we normally label [tex]\(x\)[/tex] and [tex]\(y\)[/tex] to denote different unknowns, it seems Malik should have kept [tex]\(y\)[/tex] intact and solved for [tex]\(x\)[/tex]. However, Malik has substituted 60 for [tex]\(y\)[/tex] instead of substituting 60 for [tex]\(x\)[/tex].

Therefore, the first error Malik made is in substitution, where Malik substituted 60 for [tex]\(y\)[/tex] instead of [tex]\(x\)[/tex].

So, the correct answer is:
Malik substituted 60 for [tex]\(y\)[/tex] instead of [tex]\(x\)[/tex].