Question

Solving inequalities sample work

Answer 1

To solve inequalities, we follow similar steps as solving equations but with some additional rules depending on the inequality sign.

Let's work through an example:

Solve the inequality: 3x - 4 > 8.

Step 1: Add 4 to both sides to isolate the variable.
3x - 4 + 4 > 8 + 4
3x > 12

Step 2: Divide both sides by 3 to solve for x.
3x/3 > 12/3
x > 4

Therefore, the solution to the inequality is x > 4.

It's important to note that if we multiply or divide both sides of the inequality by a negative number, we need to reverse the inequality sign:

For example: -2x < 10

Step 1: Divide both sides by -2.
(-2x)/(-2) > 10/(-2)
x < -5

So, the solution to the inequality is x < -5.