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

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

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

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

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

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

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

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

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