solve using addition and multiplication principles.
Q: 8 - 6x > 4 - 5x
the solution set is {x|x ? ?}
A: {x|x < 4}
To solve the inequality using the addition and multiplication principles, we need to isolate the variable x on one side of the inequality.
Step 1: Start by simplifying both sides of the inequality.
Simplifying the left side: 8 - 6x
Simplifying the right side: 4 - 5x
Step 2: Now, we want to isolate the variable x on one side of the inequality. We can do this by performing addition and subtraction operations to move the terms around.
Subtracting 4 from both sides: 8 - 6x - 4 > 4 - 5x - 4
Simplifying both sides further: 4 - 6x > -1 - 5x
Step 3: We can now rearrange the terms: -6x + 4 > -5x - 1.
Step 4: To get rid of the x-term from the left side, we should subtract -6x from both sides, and the same for the constant terms by subtracting 4 from both sides.
-6x + 4 - (-6x) > (-5x - 1) - (-6x)
Simplifying both sides further: 4 > x - 1
Step 5: Next, we want to isolate the variable x on one side, so let's add 1 to both sides.
4 + 1 > x - 1 + 1
Simplifying both sides further: 5 > x
Finally, we have obtained x > 5 as our solution.
However, the original question asked for the solution set in set notation form. Since the inequality is not strict (using ≥ or ≤ signs), but rather just > and <, we should use an open interval.
Thus, the solution set in set notation form for the inequality is {x | x < 5} or {x | x is less than 5}.