Solving Compound Inequalities with 'Or' (Union)

Q1. Solve the compound inequality: $-6x \leq -18$ or $6x - 24 \geq 18$

Background

Topic: Compound Inequalities (Union)

This question tests your ability to solve compound inequalities involving the word "or" and to express the solution set as a union of intervals. You need to solve each inequality separately and then combine their solution sets.

Key Terms and Formulas:

• Compound Inequality: An inequality that combines two inequalities using "and" or "or".

• Union (U): The set of all values that satisfy either inequality.

• Interval Notation: A way to represent solution sets on the real number line.

Step-by-Step Guidance

1. Start by solving the first inequality: $-6x \leq -18$.

2. Divide both sides by $-6$. Remember, dividing by a negative number reverses the inequality sign:

   $x \geq 3$

3. Now, solve the second inequality: $6x - 24 \geq 18$.

4. Add $24$to both sides to isolate the $6x$ term:

   $6x \geq 42$

5. Divide both sides by $6$to solve for$x$:

   $x \geq 7$

Try solving on your own before revealing the answer!