by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?
x2−96=4x
Step 1: x2+4x−96=0
Add 4x
to both sides.
Step 2: (x+12)(x−8)=0
Factor.
Step 3: x+12=0
or x−8=0
Use the Zero Product Property.
x=−12
or x=8
(1 point)
Responses
Step 2; she did not factor the left side of the equation correctly.
Step 2; she did not factor the left side of the equation correctly.
She did not make any mistakes.
She did not make any mistakes.
Step 1; she added 4x
to both sides instead of subtracting.
Step 1; she added 4 x to both sides instead of subtracting.
Step 3; she did not apply the Zero Product Property correctly.
1 answer
Jedida made a mistake in Step 1. The original equation is:
\[ x^2 - 96 = 4x \]
To rearrange it correctly, she should have subtracted \( 4x \) from both sides, resulting in:
\[ x^2 - 4x - 96 = 0 \]
However, she incorrectly added \( 4x \) to both sides, which led to:
\[ x^2 + 4x - 96 = 0 \]
Thus, the correct response is:
Step 1; she added 4x to both sides instead of subtracting.
