Chelsea shows her work in finding the solution to 4x − 5 = 2 + 3(x − 3). After checking her answer in the original equation, she found that it did not work. Where did she make a mistake?

Step 1: She distributed incorrectly.
Step 2: She subtracted 3x incorrectly.
Step 3: She simplified incorrectly.
Step 4: She subtracted 5 instead of adding 5.

Question

Chelsea shows her work in finding the solution to 4x − 5 = 2 + 3(x − 3). After checking her answer in the original equation, she found that it did not work. Where did she make a mistake?

Step 1: She distributed incorrectly.
Step 2: She subtracted 3x incorrectly.
Step 3: She simplified incorrectly.
Step 4: She subtracted 5 instead of adding 5.

Quizzma Team · Answer

To identify Chelsea’s mistake, let’s solve the equation step-by-step:

1. Start with the original equation:

( 4x – 5 = 2 + 3(x – 3) )

2. Distribute on the right side:

( 3(x – 3) = 3x – 9 )

So we rewrite the equation as:

( 4x – 5 = 2 + 3x – 9 )

3. Combine like terms on the right:

( 2 – 9 = -7 )

Thus, the equation becomes:

( 4x – 5 = 3x – 7 )

4. Now, isolate the variable ( x ):

Subtract ( 3x ) from both sides:

( 4x – 3x – 5 = -7 )

This simplifies to:

( x – 5 = -7 )

5. Finally, add 5 to both sides:

( x = -7 + 5 )

Which gives us:

( x = -2 )

Now, let’s analyze where Chelsea might have gone wrong:

– If she made a mistake in Step 1 (distributing incorrectly), that could lead to an incorrect equation right from the start.

– If Step 2 (subtracting ( 3

1 Answer