maliks solution to the equation $\frac{2}{5}x - 4y = 10$, when $x = 60$, is shown below.$\frac{2}{5}x - 4y = 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\
ight = \frac{5}{2}250$$x = 265$what error did malik make first when solving the equation $\frac{2}{5}x - 4y = 10$?$\bigcirc$ malik did not multiply $\frac{5}{2}(250)$ correctly.$\bigcirc$ malik added 240 to each side of the equation.$\bigcirc$ malik did not multiply $\frac{5}{2}\left(\frac{2}{5}x\
ight)$ correctly.

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# Brief Explanations:
To find the first error, we analyze each step. The original equation is $\frac{2}{5}x - 4y = 10$ with $x = 60$. The first substitution step should be replacing $x$ with $60$, but Malik incorrectly substituted $x = 60$ into the $x$ term but then made a mistake in the $y$-term? Wait, no, looking at the steps: the second line is $\frac{2}{5}x - 4(60)=10$ – but the original equation has $4y$, not $4x$. Wait, no, the equation is $\frac{2}{5}x - 4y = 10$, and we are to substitute $x = 60$, so the correct substitution is $\frac{2}{5}(60)-4y = 10$, but Malik wrote $\frac{2}{5}x - 4(60)=10$ (he substituted $60$ for $y$ instead of $x$? Wait, no, the variable is $x = 60$, so the first error is in the substitution step: he should have replaced $x$ with $60$ in $\frac{2}{5}x$, not left $x$ as is and multiplied $4$ by $60$ (which is substituting $y = 60$ incorrectly). But among the given options, let's check the options:

Wait, the options are about later steps? Wait no, the first error. Let's re-examine the steps:

Step 1: Original equation $\frac{2}{5}x - 4y = 10$

Step 2: $\frac{2}{5}x - 4(60)=10$ – here, he substituted $x = 60$ into the $y$-term (since the equation has $4y$, not $4x$), so he incorrectly replaced $y$ with $60$ instead of $x$ with $60$ in the $x$-term. But the given options don't mention that. Wait, maybe I misread. Wait the equation is $\frac{2}{5}x - 4y = 10$, and we are to solve for $y$ when $x = 60$, but Malik is solving for $x$ (the last step is $x = 265$), which is wrong. But the options given are:

1. Malik did not multiply $\frac{5}{2}(250)$ correctly.

2. Malik added 240 to each side (that step is correct, adding 240 to both sides is valid).

3. Malik did not multiply $\frac{5}{2}[\frac{2}{5}x]$ correctly (but $\frac{5}{2} \times \frac{2}{5}x = x$, which is correct).

Wait, maybe the first error is in the substitution: he should have substituted $x = 60$ into $\frac{2}{5}x$, so $\frac{2}{5}(60) = 24$, but he left $x$ as a variable and multiplied $4$ by $60$ (treating $y = 60$). But among the options, none of them mention substitution, but maybe the options are miswritten. Wait, the options given are about later steps, but the first error is in the substitution. However, among the given options, the first error in the steps shown: the second line is $\frac{2}{5}x - 4(60)=10$ – he should have $\frac{2}{5}(60) - 4y = 10$, but he kept $x$ as a variable and substituted $60$ for $y$. But the options don't have that. Wait, maybe the question is about the arithmetic in the steps. Wait the third line: $\frac{2}{5}x - 240 = 10$ – if $x$ was supposed to be 60, then $\frac{2}{5}(60) = 24$, so $24 - 4y = 10$, but Malik has $\frac{2}{5}x - 240 = 10$, which is wrong. But the options are about the later steps. Wait, the options are:

- Malik did not multiply $\frac{5}{2}(250)$ correctly: $\frac{5}{2} \times 250 = 625$, but he got $x = 265$, so that's an error, but is that the first error? No, the first error is earlier. But the options given are about the multiplication steps. Wait, maybe the question has a typo, but among the options, the first error in the steps shown (the second line is wrong, but the options don't include that). Wait, maybe I made a mistake. Let's check the options again:

Option 1: Did not multiply $\frac{5}{2}(250)$ correctly. $\frac{5}{2} \times 250 = 625$, but he got $x = 265$, so that's an error.

Option 2: Added 240 to each side – that step is correct (adding 240 to both sides is valid, so that's not an error).

Option 3: Did not multiply $\frac{5}{2}[\frac{2}{5}x]$ correctly – but $\frac{5}{2} \times \frac{2}{5}x = x$, which is correct, so that's not an error.

Wait, but the first error is in the substitution step, but since that's not an option, maybe the question is about the multiplication of $\frac{5}{2}(250)$: $\frac{5}{2} \times 250 = \frac{1250}{2} = 625$, but Malik got $x = 265$, so he did not multiply $\frac{5}{2}(250)$ correctly. So the first error among the options is option 1? Wait, no, the first error is in the substitution, but the options given are about later steps. Maybe the question's options are misaligned, but based on the options, the correct answer is the first option: Malik did not multiply $\frac{5}{2}(250)$ correctly, because $\frac{5}{2} \times 250 = 625$, but he calculated $x = 265$, which is wrong.

# Answer:
Malik did not multiply $\frac{5}{2}(250)$ correctly. (The first error among the given options is this, as adding 240 is correct, and multiplying $\frac{5}{2}[\frac{2}{5}x]$ is correct (gives $x$), so the error is in multiplying $\frac{5}{2}(250)$ which should be 625, not 265.)

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