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Creating Linear Inequalities

Creating Linear Inequalities. Introduction Inequalities are similar to equations in that they are mathematical sentences. They are different in that they are not equal all the time. An inequality has infinite solutions, instead of only having one solution like a linear equation.

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Creating Linear Inequalities

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  1. Creating Linear Inequalities

  2. Introduction Inequalities are similar to equations in that they are mathematical sentences. They are different in that they are not equal all the time. An inequality has infinite solutions, instead of only having one solution like a linear equation. Setting up the inequalities will follow the same process as setting up the equations did. Solving them will be similar, with two exceptions, which will be described later. The prefix in- in the word inequality means “not.” Remember that the symbols >, <, ≥, ≤, and ≠ are used with inequalities. 1.2.2: Creating Linear Inequalities in One Variable

  3. Key Concepts, continued 1.2.2: Creating Linear Inequalities in One Variable

  4. Vocabulary

  5. Key Concepts, continued Solving a linear inequality is similar to solving a linear equation. The processes used to solve inequalities are the same processes that are used to solve equations. Multiplying or dividing both sides of an inequality by a negative number requires reversing the inequality symbol. 1.2.2: Creating Linear Inequalities in One Variable

  6. Examples: Create an expression to represent each of the following: A number and 20 can be no more than 41 Four times some number is at most 16 The minimum value of a number is 84 45 is more than a number

  7. Key Concepts, continued 1.2.2: Creating Linear Inequalities in One Variable

  8. Guided Practice Example 1 Juan has no more than $50 to spend at the mall. He wants to buy a pair of jeans and some juice. If the sales tax on the jeans is 4% and the juice with tax costs $2, what is the maximum price of jeans Juan can afford? 1.2.2: Creating Linear Inequalities in One Variable

  9. Guided Practice: Example 1, continued Read the problem statement first. Reread the scenario and identify the known quantities. Juan has no more than $50. Sales tax is 4%. Juice costs $2. Read the statement again, identify the unknown quantity. cost of the jeans Juan has no more than $50 to spend at the mall. He wants to buy a pair of jeans and some juice. If the sales tax on the jeans is 4% and the juice with tax costs $2, what is the maximum price of jeans Juan can afford? 1.2.2: Creating Linear Inequalities in One Variable

  10. Guided Practice: Example 1, continued Create expressions and inequalities from the known quantities and variable(s). x+ 0.04x + 2 ≤ 50 1.2.2: Creating Linear Inequalities in One Variable

  11. Guided Practice: Example 1, continued Solve the problem. Normally, the answer would be rounded down to 46.15. However, when dealing with money, round up to the nearest whole cent as a retailer would. x ≤ 46.16 • x + 0.04x+ 2 ≤ 50 • 1.04x + 2 ≤ 50 • 1.04x≤ 48 • x ≤ 46.153846 • Add like terms. • Subtract 2 from both sides. • Divide both sides by 1.04. 1.2.2: Creating Linear Inequalities in One Variable

  12. Guided Practice: Example 1, continued Interpret the solution of the inequality in terms of the context of the problem. Juan should look for jeans that are priced at or below $46.16. ✔ 1.2.2: Creating Linear Inequalities in One Variable

  13. Guided Practice: Example 1, continued 1.2.2: Creating Linear Inequalities in One Variable

  14. Guided Practice Example 2 Alexis is saving to buy a laptop that costs $1,100. So far she has saved $400. She makes $12 an hour babysitting. What’s the least number of hours she needs to work in order to reach her goal? 1.2.2: Creating Linear Inequalities in One Variable

  15. Guided Practice: Example 1, continued Read the problem statement first. Reread the scenario and identify the known quantities. Needs at least $1,100 Saved $400 Makes $12 an hour Read the statement again, identify the unknown quantity. Least number of hours Alexis must work to make enough money Alexis is saving to buy a laptop that costs $1,100. So far she has saved $400. She makes $12 an hour babysitting. What’s the least number of hours she needs to work in order to reach her goal? 1.2.2: Creating Linear Inequalities in One Variable

  16. Guided Practice: Example 2, continued Create expressions and inequalities from the known quantities and variable(s). 400 + 12h ≥ 1100 1.2.2: Creating Linear Inequalities in One Variable

  17. Guided Practice: Example 2, continued Solve the problem. 400 + 12h ≥ 1100 Subtract 400 from both sides. 12h ≥ 700 Divide both sides by 12. 1.2.2: Creating Linear Inequalities in One Variable

  18. Guided Practice: Example 2, continued Interpret the solution of the inequality in terms of the context of the problem. In this situation, it makes sense to round up to the nearest half hour since babysitters usually get paid by the hour or half hour. Therefore, Alexis needs to work at least 58.5 hours to make enough money to save for her laptop. ✔ 1.2.2: Creating Linear Inequalities in One Variable

  19. Guided Practice: Example 2, continued 1.2.2: Creating Linear Inequalities in One Variable

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