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Math Pacing

Solving Inequalities by Addition and Subtraction. Math Pacing. Solving Inequalities by Addition and Subtraction. Recall that statements with greater than ( > ), less than ( < ), greater than or equal to ( ≥ ) or less than or equal to ( ≤ ) are inequalities.

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Math Pacing

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  1. Solving Inequalities by Addition and Subtraction Math Pacing

  2. Solving Inequalities by Addition and Subtraction Recall that statements with greater than (>), less than (<), greater than or equal to (≥) or less than or equal to (≤) are inequalities. Solving Inequalities by Addition and Subtraction Solving an inequality means finding values for the variable that make the inequality true. You can solve inequalities by using the Addition and Subtraction Properties of Inequalities.

  3. Solving Inequalities by Addition and Subtraction Addition and Subtraction Properties of Inequalities When you add or subtract the same value from each side of an inequality, the inequality remains true. Solving Inequalities by Addition and Subtraction

  4. Solve Then check your solution. Original inequality Add 12 to each side. This means all numbers greater than 77. Solve by Adding Example 1-1a Check Substitute 77, a number less than 77, and a number greater than 77. Answer: The solution is the set {all numbers greater than 77}.

  5. Solve Then check your solution. Answer: or {all numbers less than 14} Solve by Adding Example 1-1b

  6. Solving Inequalities by Addition and Subtraction The solution of the inequality in Example 1 was expressed as a set. A more concise way of writing a solution set is to use set-builder notation. The solution in set-builder notation is {k | k < 14}. This is read as the set of all numbers k such that k is less than 14. The solutions can be represented on a number line. Solving Inequalities by Addition and Subtraction

  7. Solve Then graph it on a number line. Original inequality Add 9 to each side. Simplify. Answer: Since is the same as y 21, the solution set is The heavy arrow pointing to the left shows that the inequality includes all the numbers less than 21. The dot at 21 shows that 21 is included in the inequality. Graph the Solution Example 1-2a

  8. Solve Then graph it on a number line. Answer: Graph the Solution Example 1-2b

  9. Solve Then graph the solution. Original inequality Subtract 23 from each side. Simplify. Answer: The solution set is Solve by Subtracting Example 1-3a

  10. Solve Then graph the solution. Answer: Solve by Subtracting Example 1-3b

  11. Solving Inequalities by Addition and Subtraction Terms with variables can also be subtracted from each side to solve inequalities. Solving Inequalities by Addition and Subtraction

  12. Then graph the solution. Original inequality Subtract 12n from each side. Simplify. Answer: Since is the same as the solution set is Variables on Both Sides Example 1-4a

  13. Then graph the solution. Answer: Variables on Both Sides Example 1-4b

  14. Solving Inequalities by Addition and Subtraction Verbal problems containing phrases like greater than or less than can often be solved by using inequalities. Solving Inequalities by Addition and Subtraction The table below shows some common verbal phrases and the corresponding mathematical inequalities.

  15. Seven timesa number is greaterthan six timesthat number minus two. 7n > 6n – 2 Original inequality Subtract 6n from each side. Simplify. Answer: The solution set is Write and Solve an Inequality Example 1-5a Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than 6 times that number minus two. Let n = the number

  16. Answer: Write and Solve an Inequality Example 1-5b Write an inequality for the sentence below. Then solve the inequality. Three times a number is less than two times that number plus 5. Let n = the number

  17. VariableLet the cost of the second pass. is less thanor equal to The total cost $100. 100 Inequality Write an Inequality to Solve a Problem Example 1-6a EntertainmentAlicia wants to buy season passes to two theme parks. If one season pass cost $54.99, and Alicia has $100 to spend on passes, the second season pass must cost no more than what amount? WordsThe total cost of the two passes must be less than or equal to $100.

  18. Original inequality Subtract 54.99 from each side. Simplify. Write an Inequality to Solve a Problem Example 1-6a Solve the inequality. Answer: The second pass must cost no more than $45.01.

  19. Write an Inequality to Solve a Problem Example 1-6b Michael scored 30 points in the four rounds of the free throw contest. Randy scored 11 points in the first round, 6 points in the second round, and 8 in the third round. How many points must he score in the final round to surpass Michael’s score? Answer: 6 points

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