is arjun’s work correct?
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.

arjun’s work
( 7x + 16 = -3x - 4 )
step 1: ( -3x )
( 4x + 16 = -4 )
step 2: ( -16 )
( -16 )
( 4x = -20 )
step 3: ( \frac{4x}{4} = \frac{-20}{4} )
( x = -5 )

( 7x + 16 = -3x - 4 )
( 7(-5) + 16 = -3(-5) - 4 )
( -35 + 16 = 15 - 4 )
( -19 = 11 )
false

Question

is arjun’s work correct?
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.

arjun’s work
( 7x + 16 = -3x - 4 )
step 1: ( -3x )
( 4x + 16 = -4 )
step 2: ( -16 )
( -16 )
( 4x = -20 )
step 3: ( \frac{4x}{4} = \frac{-20}{4} )
( x = -5 )

( 7x + 16 = -3x - 4 )
( 7(-5) + 16 = -3(-5) - 4 )
( -35 + 16 = 15 - 4 )
( -19 = 11 )
false

Accepted Answer

To determine if Arjun's work is correct, we analyze each step:

### Step 1:
Arjun starts with $ 7x + 16 = -3x - 4 $. He subtracts $ -3x $ (or adds $ 3x $) to both sides:
$ 7x + 3x + 16 = -4 $ → $ 10x + 16 = -4 $? Wait, no—Arjun’s Step 1 shows $ 4x + 16 = -3x - 3x - 4 $? Wait, no, re-examining: Arjun’s Step 1 is $ 7x + 16 - 3x = -3x - 4 - 3x $? No, the original Step 1 is $ 7x + 16 = -3x - 4 $, then he subtracts $ 3x $ from both sides? Wait, no—**Wait, the error is in Step 4**: When verifying $ x = -5 $, Arjun calculates $ 7(-5) + 16 = -35 + 16 = -19 $, and $ -3(-5) - 4 = 15 - 4 = 11 $. But $ -19
eq 11 $, so the solution is incorrect. However, the options focus on algebraic steps. Wait, re-examining the options:

- The “Yes” option is wrong (since $ -19
eq 11 $).
- Step 1: Arjun subtracts $ 3x $ (not adds) from both sides. The option says “should have added $ 3x $”—but adding $ 3x $ is equivalent to subtracting $ -3x $, and both methods (adding $ 3x $ or subtracting $ 3x $) are valid? Wait, no—let’s redo the equation:

Original equation: $ 7x + 16 = -3x - 4 $.

To isolate $ x $, we can add $ 3x $ to both sides: $ 7x + 3x + 16 = -4 $ → $ 10x + 16 = -4 $.

Or subtract $ 7x $: $ 16 = -10x - 4 $.

But Arjun’s Step 1: $ 7x + 16 - 3x = -3x - 4 - 3x $ → $ 4x + 16 = -6x - 4 $? Wait, no, the image shows Step 1 as $ 4x + 16 = -4 $, which is incorrect. Wait, no—maybe the key error is in Step 4’s verification, but the options are about algebraic steps. Wait, the option “No. In Step 4, Arjun subtracted 16 from −4 incorrectly” doesn’t match. Wait, re-reading the options:

The correct error is in **Step 4’s verification**, but the options given: Wait, the last option (fifth) is “No. In Step 4, Arjun subtracted 16 from −4 incorrectly.” Wait, no—when verifying $ x = -5 $, Arjun computes $ 7(-5) + 16 = -35 + 16 = -19 $, and $ -3(-5) - 4 = 15 - 4 = 11 $. But the option about Step 4 says “Arjun subtracted 16 from −4 incorrectly”—no, the error is in the verification, but the options are about algebraic steps. Wait, the correct option is the one about Step 4? No, re-examining the options:

Wait, the options are:

1. Yes. The value of $ x $ is $ -5 $. (Incorrect, since $ -19
eq 11 $.)
2. No. In Step 1, Arjun should have added $ 3x $ on both sides to help isolate $ x $. (Adding $ 3x $ is valid, but Arjun subtracted $ 3x $; both are valid, so this is not the error.)
3. No. In Step 2, Arjun subtracted $ 3x $ from $ 7x $ incorrectly. (Step 2: $ 4x + 16 = -4 $ → he subtracts 16: $ 4x = -20 $. Wait, no—Step 2 is $ 4x + 16 = -4 $, then Step 3: subtract 16: $ 4x = -20 $. Step 4: divide by 4: $ x = -5 $. But verification fails. However, the error in verification is because $ x = -5 $ is not a solution. But the options about the steps: the “No. In Step 4, Arjun subtracted 16 from −4 incorrectly” is not about the algebraic steps, but the verification. Wait, the key is: when solving $ 7x + 16 = -3x - 4 $, let's solve it correctly:

1. Add $ 3x $ to both sides: $ 10x + 16 = -4 $.
2. Subtract 16: $ 10x = -20 $.
3. Divide by 10: $ x = -2 $.

Arjun’s Step 1: He subtracts $ 3x $ from both sides: $ 7x - 3x + 16 = -3x - 3x - 4 $ → $ 4x + 16 = -6x - 4 $. Wait, that’s the error! Oh, I misread Step 1. Arjun’s Step 1 is $ 7x + 16 - 3x = -3x - 4 - 3x $, which simplifies to $ 4x + 16 = -6x - 4 $, but he wrote $ 4x + 16 = -4 $. So he incorrectly subtracted $ 3x $ from $ -3x $ (on the right side) as $ -3x - 3x = -6x $, but he wrote $ -4 $ (missing the $ -6x $). Wait, no—the image shows Step 1 as $ 4x + 16 = -4 $, so he incorrectly simplified the right side. But the options:

The option “No. In Step 2, Arjun subtracted 3x from 7x incorrectly” is not right. Wait, the correct option is the one about Step 4? No, the verification shows $ -19 = 11 $ (false), but the options are about algebraic steps. Wait, the first “No” option: “No. In Step 4, Arjun subtracted 16 from −4 incorrectly”—no, Step 4 is dividing $ 4x = -20 $ by 4, which is correct. The error is in the verification, but the options:

Wait, the correct answer is the option: **No. In Step 4, Arjun subtracted 16 from −4 incorrectly**? No, the verification step (Step 4 of the check) has $ -35 + 16 = -19 $ and $ 15 - 4 = 11 $, so $ -19 = 11 $ is false, meaning the solution is wrong. But the options: the first “Yes” is wrong. The next option: “No. In Step 1, Arjun should have added 3x on both sides to help isolate x”—adding 3x is a valid step (to get $ 10x + 16 = -4 $), while Arjun subtracted 3x (leading to $ 4x + 16 = -6x - 4 $, which he then mis-simplified). But the option says “should have added 3x”—this is correct, because adding 3x is a more direct way to isolate x (eliminating the $ -3x $ on the right). However, the key error is in the verification, but the options:

Wait, the correct answer is the option: **No. In Step 4, Arjun subtracted 16 from −4 incorrectly**? No, the verification step shows $ -35 + 16 = -19 $ and $ 15 - 4 = 11 $, so $ -19
eq 11 $, meaning the solution is wrong. But the options: the first “Yes” is wrong. The next option: “No. In Step 1, Arjun should have added 3x on both sides to help isolate x”—this is the correct reasoning, but wait, let's re-express:

Original equation: $ 7x + 16 = -3x - 4 $.

To solve for $ x $, we can add $ 3x $ to both sides (to eliminate $ -3x $ on the right):

$ 7x + 3x + 16 = -4 $ → $ 10x + 16 = -4 $.

Arjun instead subtracted $ 3x $ from both sides, leading to $ 4x + 16 = -6x - 4 $ (but he incorrectly wrote $ 4x + 16 = -4 $, missing the $ -6x $). However, the option “No. In Step 1, Arjun should have added 3x on both sides to help isolate x” is correct, because adding $ 3x $ is a standard step to combine like terms (eliminating the $ x $-term on the right).

Wait, no—let’s check the options again:

- **Yes. The value of $ x $ is $ -5 $.** → Incorrect (verification fails).
- **No. In Step 1, Arjun should have added $ 3x $ on both sides to help isolate $ x $.** → Correct. Because subtracting $ 3x $ (as Arjun did) leads to a more complicated equation, while adding $ 3x $ (to both sides) simplifies it to $ 10x + 16 = -4 $, which is easier to solve. Arjun’s Step 1 was incorrect in the operation (subtracting $ 3x $ instead of adding $ 3x $) to isolate $ x $.

# Brief Explanations:
Arjun’s solution is incorrect. In Step 1, adding $ 3x $ to both sides (instead of subtracting $ 3x $) is the correct approach to isolate $ x $ (eliminating the $ -3x $ term on the right). Verification shows $ x = -5 $ does not satisfy the original equation.

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

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