Let's start by solving the equation step-by-step to identify Malik's error.
Given the equation:
[tex]\[
\frac{2}{5}x - 4y = 10
\][/tex]
We know that [tex]\(x = 60\)[/tex]. Substitute [tex]\(x = 60\)[/tex] into the equation:
[tex]\[
\frac{2}{5}(60) - 4y = 10
\][/tex]
Compute [tex]\(\frac{2}{5}(60)\)[/tex]:
[tex]\[
\frac{2 \times 60}{5} = \frac{120}{5} = 24
\][/tex]
The equation then becomes:
[tex]\[
24 - 4y = 10
\][/tex]
Now, isolate the term involving [tex]\(y\)[/tex]:
1. Subtract 24 from both sides:
[tex]\[
24 - 4y - 24 = 10 - 24
\][/tex]
Which simplifies to:
[tex]\[
-4y = -14
\][/tex]
2. Divide both sides by -4 to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-14}{-4} = \frac{14}{4} = \frac{7}{2} = 3.5
\][/tex]
Therefore, [tex]\(y = 3.5\)[/tex].
Now let's review the steps Malik took:
Initial Equation:
[tex]\[
\frac{2}{5} x - 4y = 10
\][/tex]
After substituting [tex]\(x = 60\)[/tex]:
[tex]\[
\frac{2}{5} (60) - 4y = 10
\][/tex]
Malik's mistake appears:
[tex]\[
\frac{2}{5} x - 4(60) = 10
\][/tex]
In this step:
[tex]\[
\frac{2}{5} x - 240 = 10
\][/tex]
It's clear that Malik wrongly substituted [tex]\(4y\)[/tex] with [tex]\(4(60)\)[/tex] instead of computing the correct value [tex]\(\frac{2}{5}(60)\)[/tex].
Continuing from Malik’s incorrect substitution:
[tex]\[
\frac{2}{5} x - 240 + 240 = 10 + 240
\][/tex]
This step implies adding 240 to both sides, attempting to eliminate -240. Hence, it compounds the mistake already made.
Therefore, the first error Malik made was incorrectly substituting [tex]\(-4y\)[/tex] with [tex]\(-4(60)\)[/tex]. This should actually only involve the substitution [tex]\(\frac{2}{5} (60) = 24\)[/tex].
To summarize:
First Error: Malik incorrectly substituted [tex]\(-4(60)\)[/tex] instead of correctly using [tex]\(\frac{2}{5}x - 4y\)[/tex]. Then continued with adding 240 to both sides needlessly:
\[\frac{2}{5} x - 4 (60) =10 \\
Therefore, the first mistake made was adding 240 to each side of the equation.
