Section 5.3 Day 1 Solving Multi-Step Inequalities Algebra 1

Learning Targets Define an inequality Solve a multi-step inequality Graph an inequality on the number line Identify the difference between no solution, all solutions, and a set of solutions

Inequality An open sentence that contains <, >, ≤, or ≥. It shows the unequal relationship between two sets

Inequality Example: 𝟒𝒙<𝟗 Example: 𝟏 𝟑 𝒙−𝟏≥−𝟏𝟓

Example 1: SOlve Solve −𝟏𝟏𝒚−𝟏𝟑>𝟒𝟐 1. −𝟏𝟏𝒚−𝟏𝟑>𝟒𝟐 2. −𝟏𝟏𝒚>𝟓𝟓 3. 𝒚<−𝟓 (KEY! Flip the sign when dividing or multiplying by a negative number!)

Example 2: Graph Graph 𝒚<−𝟓 on a number line

Example 3 Solve & graph 𝟒 𝟑𝒕−𝟓 +𝟕≥𝟖𝒕+𝟑 1. 𝟏𝟐𝒕−𝟐𝟎+𝟕≥𝟖𝒕+𝟑 2. 𝟏𝟐𝒕−𝟏𝟑≥𝟖𝒕+𝟑 3. 𝟒𝒕−𝟏𝟑≥𝟑 4. 𝟒𝒕≥𝟏𝟔 5. 𝒕≥𝟒

Example 4 Solve & graph 𝟔 𝟓𝒛−𝟑 ≤𝟑𝟔𝒛 1. 𝟑𝟎𝒛−𝟏𝟖≤𝟑𝟔𝒛 2. −𝟏𝟖≤𝟔𝒛 3. −𝟑≤𝒛

Example 5 Solve 𝟗𝒕−𝟓 𝒕−𝟓 ≤𝟒(𝒕−𝟑) 1. 𝟗𝒕−𝟓𝒕+𝟐𝟓≤𝟒𝒕−𝟏𝟐 2. 𝟒𝒕+𝟐𝟓≤𝟒𝒕−𝟏𝟐 3. 𝟐𝟓≤−𝟏𝟐 FALSE! No Solution

Example 6 Solve 𝟑 𝟒𝒎+𝟔 ≤𝟒𝟐+𝟔(𝟐𝒎−𝟒) 1. 𝟏𝟐𝒎+𝟏𝟖≤𝟒𝟐+𝟏𝟐𝒎−𝟐𝟒 2. 𝟏𝟐𝒎+𝟏𝟖≤𝟏𝟐𝒎+𝟏𝟖 Always true. Many Solutions!

Example 7 Write an inequality that describes the situation: I can only spend $𝟒𝟎 to buy clothes before taxes. Shirts, s, cost $𝟕 and pants, p, costs $𝟏𝟓. 𝟕𝒔+𝟏𝟓𝒑≤𝟒𝟎

Exit Ticket For FEedback Solve and graph the inequality 𝟖𝒂+𝟐 𝟏−𝟓𝒂 ≤𝟐𝟎