4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much...
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Transcript of 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much...
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