Step 1 4x+5<6x+1 given
Step 2 -2x+5<1. Subtraction
Step 3. -2x<6. Addition
Step 4. X>-3 division. In which step did she first make a mistake
In Step 3, there appears to be a mistake. When subtracting 6x from both sides of the inequality in Step 1, it should result in -2x + 5 < -6 rather than -2x < 6.
The mistake was made in Step 2.
The correct step should be:
Step 2: Subtract 4x from both sides:
4x + 5 < 6x + 1
-4x -4x
----------------------
5 < 2x + 1
So, the corrected inequality is 5 < 2x + 1.
In Step 3, she made the first mistake. Let's go through the steps to find out the correct solution.
Step 1: Given inequality is 4x + 5 < 6x + 1.
Step 2: To isolate the variable term, we can start by subtracting 4x from both sides of the inequality:
4x - 4x + 5 < 6x - 4x + 1,
Simplifying: 5 < 2x + 1.
Step 3: Next, we can further isolate the variable term by subtracting 1 from both sides:
5 - 1 < 2x + 1 - 1,
Simplifying: 4 < 2x.
Now, at this point, we can see that the mistake was made. In Step 3, she incorrectly subtracted 1 from the right-hand side only, but the same operation needs to be performed on both sides of the equation.
The correct Step 3 should be:
4 - 1 < 2x - 1,
Simplifying: 3 < 2x - 1.
Step 4: We can now solve for x by adding 1 to both sides of the inequality:
3 + 1 < 2x - 1 + 1,
Simplifying: 4 < 2x.
Step 5: Finally, we can solve for x by dividing both sides by 2:
4/2 < (2x)/2,
Simplifying: 2 < x.
Therefore, the correct solution is x > 2, and the mistake was made in Step 3 by only subtracting 1 from one side of the inequality.