4.1.2 – Compound Inequalities

• Recall from yesterday, to solve a linear-inequality, we solve much like we solve an equation– Isolate the variable– Inverse operations– Flip sign when multiply/divide by a negative

number– Open vs. Closed dots

Compound Inequalities

• We can combine different inequalities to form compound inequalities

• Two cases to consider

• 1) AND

• 2) OR

AND

• An “AND” inequality will be one of the form

• a < x < b OR a ≤ x ≤ b

• On the number line:

• To solve an AND problem, we usually keep it as one inequality

• Basically like operating with two equal signs• What we do to the middle, we must do to

BOTH sides

• If you divide or multiply by a negative number, BOTH signs will flip

• Example. Solve the inequality 4 < x + 5 < 7. Graph your solutions on a number line.

• Example. Solve the inequality -8 ≤ x – 10 ≤ -2. Graph your solutions on a number line.

• Example. Solve the inequality -1 ≤ -m + 2 ≤ -3. Graph your solutions on a number line.

OR

• With an OR problem, we will essentially have two separate inequalities

• x < a OR x > b

• Graph of solutions:

• Example. Solve the inequality 3x + 2 < 8 OR 2x – 9 > 3. Graph your solutions on the number line.

• Example. Solve the inequality -x > 4 OR -2x – 6 < 0. Graph your solutions on the number line.

• Assignment• Pg. 176• 34-37, 40-42, 49-56, 61