Inequalities

Question 1

Define these:

1. a < b
2. a ≤ b
3. a > b
4. a ≥ b

Answer 1

1. a is strictly less than b
2. a is less than or equal to b
3. a is strictly greater than b
4. a is greater than or equal to b

Question 2

What are the following written as in set notation?

1. x > 2

2. x > 1 and x ≤ 4

3. x ≤ 1 or x > 5

Answer 2

1. { x∈ℝ: x > 2 }

2. { x∈ℝ: 1 < x ≤ 4 }

3. { x∈ℝ: x ≤ 1 } ∪ { x∈ℝ: x > 5 }

Question 3

What method do you use to solve quadratic inequalities?

Answer 3

1) Solve the quadratic to find critical values

2) Sketch the quadratic, labelling critical values

3) Shade the region satisfying the inequality

4) Set Notation for your final answer

Question 4

How do you shade inequalities on graphs?

Answer 4

• Draw ≥ or ≤ inequalities with a solid line

• Draw > or < inequalities with a dashed line

• Shade the region that satisfies the stated inequalities.