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

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4.1.2 – Compound Inequalities

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

Page 1: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

4.1.2 – Compound Inequalities

Page 2: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

• 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

Page 3: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

Compound Inequalities

• We can combine different inequalities to form compound inequalities

• Two cases to consider

• 1) AND

• 2) OR

Page 4: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

AND

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

• a < x < b OR a ≤ x ≤ b

• On the number line:

Page 5: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

• 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

Page 6: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

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

Page 7: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

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

Page 8: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

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

Page 9: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

OR

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

• x < a OR x > b

• Graph of solutions:

Page 10: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

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

Page 11: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

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

Page 12: 4.1.2 – Compound Inequalities. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable –

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