Question

arjun is solving the equation (7x + 16 = -3x - 4). his work is shown.
is arjun’s work correct?
arjun’s 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.

Explanation:

Step1: Verify Step 1 of Arjun's work

Original equation: $7x + 16 = -3x - 4$
Arjun subtracts $3x$: $7x - 3x + 16 = -3x - 3x - 4$ → $4x + 16 = -6x - 4$, but Arjun wrote $4x + 16 = -4$. This is wrong. The correct operation is to add $3x$ to both sides: $7x + 3x + 16 = -3x + 3x - 4$ → $10x + 16 = -4$.

Step2: Evaluate the options

Arjun made an error in Step 1 by subtracting $3x$ instead of adding $3x$ to isolate $x$.

Answer:

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