Step 1: 4x + 5 < 6x + 1 (Given)
Step 2: -2x + 5 < 1 (Subtraction)
Step 3: -2x < 6 (Addition)
Step 4: x > -3 (Division)
Mia is trying to find her mistake in the problem shown. In which step did she first make a mistake?
A. Step 1
B. Step 2
C. Step 3
D. Step 4
The correct answer is D. Step 4.
In step 4, Mia divided by -2 without properly flipping the inequality sign. When dividing by a negative number, the direction of the inequality should be reversed. Therefore, the correct step should be x < -3, not x > -3.
In this case, we can identify the mistake by comparing each step in Mia's work with the correct way to solve the inequality 4x + 5 < 6x + 1.
Let's go through each step and determine the correct approach:
Step 1: 4x + 5 < 6x + 1 (Given)
This step is correct. Mia wrote the given inequality correctly.
Step 2: -2x + 5 < 1 (Subtraction)
This step is incorrect. To isolate x terms, Mia should subtract 4x from both sides, not subtract 5.
The correct step would be: 4x - 4x + 5 < 6x - 4x + 1, which simplifies to 5 < 2x + 1.
Therefore, the answer is:
B. Step 2
To find the mistake, we need to carefully analyze each step one by one and see if the transformation made is correct.
Step 1: 4x + 5 < 6x + 1 (Given)
Step 2: -2x + 5 < 1 (Subtraction: subtracting 6x from both sides)
Step 3: -2x < 6 (Addition: subtracting 5 from both sides)
Step 4: x > -3 (Division: dividing both sides by -2)
To determine the mistake, let's work through the problem again:
Starting with Step 1: 4x + 5 < 6x + 1
Let's subtract 4x from both sides: 5 < 2x + 1
Now, let's subtract 1 from both sides: 4 < 2x
Next, we divide both sides by 2, it should look like this: 2 < x
However, in Step 3, Mia mistakenly subtracted 5 from both sides instead of subtracting 4x from both sides. This mistake caused a wrong equation in Step 4.
Therefore, the mistake Mia made was in Step 3.
The correct answer is:
C. Step 3.