is arjuns work correct?
arjuns work
7x + 16 = -3x - 4
- 3x - 3x step 1
4x + 16 = -4 step 2
- 16 - 16 step 3
4x = -20 step 4
\frac{4x}{4} = \frac{-20}{4}
x = -5
options:
yes. the value of x is -5.
no. in step 1, arjun should have added 3x on both sides to help isolate x.
no. in step 2, arjun subtracted 3x from 7x incorrectly.
no. in step 3, arjun should have added 16 on both sides to help isolate x.
no. in step 4, arjun subtracted 16 from -4 incorrectly.

Question

is arjuns work correct?
arjuns work
7x + 16 = -3x - 4
- 3x    - 3x  step 1
4x + 16 = -4  step 2
 - 16  - 16  step 3
 4x = -20     step 4
\frac{4x}{4} = \frac{-20}{4}
x = -5
options:
yes. the value of x is -5.
no. in step 1, arjun should have added 3x on both sides to help isolate x.
no. in step 2, arjun subtracted 3x from 7x incorrectly.
no. in step 3, arjun should have added 16 on both sides to help isolate x.
no. in step 4, arjun subtracted 16 from -4 incorrectly.

Accepted Answer

Explanation:
## Step1: Analyze Step 1
Arjun started with $7x + 16=-3x - 4$. He subtracted $3x$ from both sides. Let's check the correct way to isolate $x$. To get all $x$ terms on one side, we can add $3x$ to both sides (since $-3x+3x = 0$) or subtract $7x$. But subtracting $3x$ from $7x$ gives $4x$, which is correct. Wait, no—wait, the equation is $7x+16=-3x - 4$. If we subtract $3x$ from both sides: left side $7x - 3x+16 = 4x + 16$, right side $-3x-3x - 4=-6x - 4$. Wait, that's wrong! Wait, no, Arjun's Step 2 is $4x + 16=-4$. Wait, that means he made a mistake in Step 1. Wait, no—wait, let's redo the equation.

Wait, original equation: $7x + 16=-3x - 4$. To solve for $x$, we can add $3x$ to both sides: $7x+3x + 16=-3x + 3x-4$, which is $10x + 16=-4$. Or subtract $7x$: $16=-10x - 4$. But Arjun subtracted $3x$ from both sides: $7x-3x + 16=-3x-3x - 4$ → $4x + 16=-6x - 4$. But his Step 2 is $4x + 16=-4$, which means he messed up the right side. Wait, no—wait, maybe I misread. Wait, Arjun's Step 1: subtract $3x$ from both sides. So left side: $7x - 3x+16 = 4x + 16$. Right side: $-3x-3x - 4=-6x - 4$. But his Step 2 is $4x + 16=-4$, which is incorrect. Wait, no—wait, the correct approach: to isolate $x$, we should add $3x$ to both sides (because $-3x + 3x = 0$) to get $7x+3x + 16=-4$, so $10x+16=-4$. But Arjun subtracted $3x$, which led to a wrong right side. Wait, but let's check the answer. Wait, Arjun got $x = - 5$. Let's plug $x=-5$ into the original equation: left side $7(-5)+16=-35 + 16=-19$. Right side $-3(-5)-4 = 15 - 4 = 11$. Wait, that's not equal. Wait, no—wait, maybe I made a mistake. Wait, no, if $x=-5$, original equation: $7(-5)+16=-35 + 16=-19$; $-3(-5)-4 = 15 - 4 = 11$. So they are not equal. Wait, but maybe my calculation is wrong. Wait, no—wait, let's solve the equation correctly.

Correct solution:

$7x + 16=-3x - 4$

Add $3x$ to both sides: $7x+3x + 16=-3x+3x - 4$ → $10x + 16=-4$

Subtract 16 from both sides: $10x=-20$

Divide by 10: $x=-2$. Wait, that's different. Wait, but Arjun's steps:

Step 1: $7x + 16-3x=-3x - 4-3x$ → $4x + 16=-6x - 4$ (but he wrote $4x + 16=-4$, which is wrong). Wait, maybe the problem is in Step 1. Wait, the options: let's check the options.

Option 2: "No. In Step 1, Arjun should have added 3x on both sides to help isolate x." Let's see: if he adds 3x, then $7x+3x + 16=-3x+3x - 4$ → $10x + 16=-4$, which is a better way to isolate x (since we eliminate the $-3x$ on the right). Arjun subtracted 3x, which kept a $-6x$ on the right (but he incorrectly wrote $-4$ instead of $-6x - 4$ in Step 2). Wait, but the option says "In Step 1, Arjun should have added 3x on both sides". Let's check the other options.

Option 3: "No. In Step 2, Arjun subtracted 3x from 7x incorrectly." $7x - 3x = 4x$, which is correct. So Step 2's left side is correct, but right side is wrong. Wait, Arjun's Step 2 is $4x + 16=-4$, but after Step 1 (subtracting 3x), the right side should be $-3x - 4-3x=-6x - 4$, not $-4$. So Step 2's right side is wrong, but the option about Step 1: adding 3x is a better approach. Wait, maybe the intended error is in Step 1. Let's re-express the equation.

To solve $7x + 16=-3x - 4$, the standard method is to add $3x$ to both sides to get $10x + 16=-4$, then subtract 16: $10x=-20$, $x=-2$. But Arjun subtracted $3x$, leading to $4x + 16=-6x - 4$ (but he wrote $4x + 16=-4$ in Step 2, which is a mistake). But the option says "In Step 1, Arjun should have added 3x on both sides". Let's check the steps again.

Wait, maybe the problem is that when Arjun subtracted 3x, he made a mistake in the right side. But the option 2 is about Step 1: he should have added 3x. Let's see: if he adds 3x, then the right side becomes $-4$ (since $-3x + 3x = 0$), which is what he wrote in Step 2 (but he subtracted 3x, which is wrong). So the correct option is option 2: "No. In Step 1, Arjun should have added 3x on both sides to help isolate x."

Wait, but let's check Arjun's final answer: he got $x=-5$, but if we solve correctly, $x=-2$. Wait, maybe I messed up. Wait, let's do Arjun's steps again:

Step 1: $7x + 16-3x=-3x - 4-3x$ → $4x + 16=-6x - 4$ (but he wrote $4x + 16=-4$, so Step 2 is wrong). But the option 2 says Step 1 is wrong. Maybe the problem is that subtracting 3x is not the best way, and adding 3x is better. Let's check the options again.

Option 2: "No. In Step 1, Arjun should have added 3x on both sides to help isolate x." Let's see: adding 3x would eliminate the $-3x$ on the right, so $7x+3x + 16=-3x+3x - 4$ → $10x + 16=-4$, which is a valid step. Arjun subtracted 3x, which led to a more complicated equation (with $-6x$ on the right), but he incorrectly simplified the right side to $-4$ (missing the $-6x$). But the option is about Step 1: he should have added 3x. So this option is correct.

# Answer:
B. No. In Step 1, Arjun should have added 3x on both sides to help isolate x.

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Step1: Analyze Step 1

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