1. U1A L6 Linear, Quadratic & Polynomial Inequalities
UNIT 1A LESSON 6A
Linear, Inequalities

2. INTERVALS & INEQUALITIES
U1A L6 Linear, Quadratic & Polynomial Inequalities
INTERVALS & INEQUALITIES
Interval
Notation
Inequality
Notation
Graph

3. U1A L6 Linear, Quadratic & Polynomial Inequalities
Express the following intervals in terms of inequalities
and graph the intervals

4. U1A L6 Linear, Quadratic & Polynomial Inequalities
REMEMBER:
Linear inequalities are solved the same as equations
EXCEPT
when a step involves multiplying or dividing by a NEGATIVE.
You must change the direction of the sign.
U1A L6 Linear, Quadratic & Polynomial Inequalities
𝟕+𝟑 −𝟐 <𝟒
𝟏𝟎>𝟒
−𝟐 𝟏 𝟕+𝟑 −𝟐 > −𝟐 𝟒
𝟏𝟎 −𝟐 < 𝟒 −𝟐
𝟏𝟎>−𝟖
−𝟓<−𝟐

5. U1A L6 Linear, Quadratic & Polynomial Inequalities
Linear Inequalities
Solve the inequalities.
State the answer in inequality
form, interval form and graph.
EXAMPLE 1
5x + 7 > – 8
5x > – 15
x > – 3 inequality form
[– 3, ∞) interval form
(−𝟑, −𝟖)
𝒀 𝟐 =−𝟖
𝒀 𝟐 =𝟓𝒙 +𝟕 -3
graph

6. U1A L6 Linear, Quadratic & Polynomial Inequalities
Linear Inequalities
Solve the inequalities.
State the answer in inequality form, interval form and graph.
EXAMPLE 2
𝒀 𝟏 =𝟑𝒙 +𝟏
3x + 1 < 7x – 7
– 4x < – 8
x > 2 inequality form
(𝟐, 𝟕)
(2, ∞) interval form 2
graph
𝒀 𝟐 =𝟕𝒙−𝟕

7. U1A L6 Linear, Quadratic & Polynomial Inequalities
Linear Inequalities
Solve the inequalities and graph.
State the answer in inequality form and interval form.
𝒀 𝟏 =𝟖−𝒙
𝒀 𝟐 =𝟓𝒙+𝟐
EXAMPLE 3
8 – x > 5x + 2
(𝟏, 𝟕)
– 6x > – 6
−𝟔𝒙 −𝟔 < −𝟔 −𝟔
x < 1 inequality form
(–∞, 1) interval form 1
graph

8. U1A L6 Linear, Quadratic & Polynomial Inequalities
Linear Inequalities
Solve the inequalities and graph.
State the answer in inequality form and interval form.
EXAMPLE 4
x >12 inequality form
𝟒−𝟐𝒙 𝟓 ≤−𝟒
[12, ∞) interval form
𝟓 𝟏 𝟒−𝟐𝒙 𝟓 ≤ 𝟓 −𝟒
graph
𝟒−𝟐𝒙≤−𝟐𝟎 12
−𝟐𝒙≤−𝟐𝟒
−𝟐𝒙 −𝟐 ≤ −𝟐𝟒 −𝟐
𝒙≥𝟏𝟐

9. U1A L6 Linear, Quadratic & Polynomial Inequalities
Linear Inequalities
Solve the inequalities and graph.
State the answer in inequality form and interval form.
EXAMPLE 5
𝒙 <−𝟏𝟕 inequality form
𝟑+𝒙 −𝟐 >𝟕
(−𝟏𝟕, ∞) interval form
−𝟐 𝟏 𝟑+𝒙 −𝟐 < −𝟐 𝟕
graph
𝟑+𝒙<−𝟏𝟒
-17
𝒙<−𝟏𝟕