How can we solve the inequality 24x – 3 ≥ -3 – 3x + 5x?

To solve the inequality 24x – 3 ≥ -3 – 3x + 5x, we will first simplify the right side of the inequality. Let’s break it down step by step:

1. Simplifying the right side: Combine the terms on the right side:

-3 – 3x + 5x simplifies to -3 + 2x.

2. Rewriting the inequality:

Now we rewrite the original inequality with the simplified right side:

24x – 3 ≥ -3 + 2x

3. Add 3 to both sides:

To isolate the variable terms, we first add 3 to both sides of the inequality:

24x – 3 + 3 ≥ -3 + 3 + 2x

This simplifies to:

24x ≥ 2x

4. Subtract 2x from both sides:

Next, we will subtract 2x from both sides to further isolate the x variable:

24x – 2x ≥ 0

This results in:

22x ≥ 0

5. Dividing both sides by 22:

Finally, we divide both sides by 22:

x ≥ 0

Thus, the solution to the inequality 24x – 3 ≥ -3 – 3x + 5x is:

x ≥ 0

This means that any value of x that is 0 or greater satisfies the original inequality.