solving problem involve linear inequality.pptx

linear inequality

1. To simplify the solutions, remember the following steps below. Steps in Solving Problems Involving Linear Inequalities in Two Variables Step 1 : Identify the words needed to be represented with variables/symbols. Step 2 : Translate the statement into mathematical expression. Step 3 : Identify what is asked in the problem then solve.

2. Illustrative Example 1. Your parents give you a weekly allowance greater than 𝑃200. The allowance is budgeted for your food and school needs. If you allotted 𝑃70 for your school needs, what would be the minimum budget for your food? Solution: Step 1: Identify the words needed to be represented with variables/symbols. Let 𝑥 represents the budget for the school needs Let 𝑦 represents the budget for food The symbol for greater than is “>”

3. Step 2: Translate the statement into mathematical expression. 𝑥 + 𝑦 > 200 Step 3: Identify what is asked in the problem then solve. Solve for 𝑦 given 𝑥=70 𝑥 + 𝑦 > 200 Given 𝑥 − 𝑥 + 𝑦 > 200 − 𝑥 By adding the additive inverse on both sides of the inequality 𝑦 > 200 − 𝑥 By simplifying 𝑦 > 200 − 70 By substituting 𝑥 = 70 𝑦 > 130 Simplified form This means that the minimum budget for the food in a week is ₱ 130.

4. Illustrative Example 2 In a week, Martinez family spends less than ₱3,021 for food (𝑓) and educational expense (𝑒). Suppose the family spent ₱1000 for education, what could be the family’s maximum possible expenses for food?

5. Illustrative Example 3 The difference between the height of Mark (𝑚) and Rhea (𝑟) is at least 5 cm. If Rhea’s height is 160 cm, what is the least possible height of Mark?

6. Illustrative Example 4 Abby enjoys gardening. She has snake plant and rose plant in her garden. Every snake plant requires 0.5 liters of water and every rose plant requires 0.3 liters of water. Abby has a maximum of 5 liters of water for watering the snake plants and the rose plants. If Abby waters 10 rose plants, how many snake plants can she water at most with the amount of water left?