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?
Responses
Mia first made a mistake in step 3: −2x < 6 (Addition).
Mia made her mistake in Step 2: −2x + 5 < 1 (Subtraction). She incorrectly subtracted 5 from both sides of the inequality. The correct step should have been −2x < -4, not −2x + 5 < 1.
To find the mistake in the problem, we need to go through each step and check for any errors.
Step 1: 4x + 5 < 6x + 1 (Given)
This step is correct. Mia correctly rewrote the given inequality.
Step 2: −2x + 5 < 1 (Subtraction)
In this step, Mia correctly subtracted 4x from both sides of the inequality. There is no mistake here.
Step 3: −2x < 6 (Addition)
In this step, Mia correctly subtracted 5 from both sides of the inequality. There is no mistake here.
Step 4: x > −3 (Division)
Here, Mia divided both sides of the inequality by -2. However, she made a mistake while dividing the negative number. When dividing by a negative number, we need to flip the inequality sign. So, the correct step should be x < -3 instead of x > -3.
Therefore, Mia made a mistake in Step 4 by not flipping the inequality sign when dividing by a negative number.