Question

Ruby claims to have correctly solved 3 ( x 4 ) = 1 − ( 2 x − 9 ) using the steps below. step 1: 3 x 12 = 1 − ( 2 x − 9 ) step 2: 3 x 12 = 1 − 2 x − 9 step 3: 3 x 12 = − 8 − 2 x step 4: 5 x 12 = − 8 step 5: 5 x = − 20 step 6: x = − 4 one of ruby’s steps contains a mistake. which step is incorrect? A. Step 1

B. Step 2
C. Step 3
D. Step 4

Answer 1

The mistake in Ruby's steps lies in Step 2, where the negative sign was not correctly distributed, failing to change -9 to +9 after removing the parentheses.

Step-by-step explanation:

You have identified an error in Ruby's solution to the equation 3 ( x 4 ) = 1 - ( 2 x - 9 ). To find the mistake, let's review her steps:

1. Step 1: 3 x 12 = 1 - ( 2 x - 9 )
2. Step 2: 3 x 12 = 1 - 2 x + 9
3. Step 3: 3 x 12 = 10 - 2 x
4. Step 4: 5 x 12 = 10
5. Step 5: 5 x = - 2
6. Step 6: x = -4

The mistake is in Step 2. When distributing the negative sign inside the parentheses, the -9 should become +9, not remain -9. The correct Step 2 should read 3 x 12 = 1 - 2 x + 9. Therefore, the incorrect step is Step 2, which means the answer is B. Step 2.