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.
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