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Solving inequalities. mc-TY-inequalities-2009-1. Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality. In this unit inequalities are solved by using algebra and by using graphs.
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to both sides of an inequality, you must justify your work in terms of the increasing or decreasing nature of the function in question. When solving inequalities, one must be careful when multiplying both sides by a quantity which might potentially be negative. Example 4. Solve the following inequality and prove your an-swer. (4) x x+1 ≥ 1
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Oct 5, 2020 · ater than or equal to 1. Some of the val. than or equal to -8”“x” can be of any value as long as it is. ess than or equal to -8. Some of the values. 9, -14, etc.Problem 2:Give the meaning of the inequality stateme. , and determine 3. tc.Writing InequalitiesThe table below shows the words tha. less than.
Definition 8.1. Two inequalities are equivalent if they have the same solution set. Operations that Produce Equivalent Inequalities. Add or Subtract the same value on both sides of the inequality. Multiply or Divide by the same positive value on both sides of the inequality. Multiply or Divide by the same negative value on both sides of the ...
For the following examples we will use both, as this allows us to make the connections between the algebra and the graphs. Solve 3 2x 1. This is a linear inequality. Remember to reverse the inequality sign when multiplying or dividing by a negative number. Solve x2 4x + 3 < 0. This is a quadratic inequality.
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Example 2x+ 1 3 is an inequality. The solution of an inequality is the set of all numbers which satisfy the inequality. This set may have in nitely many numbers and may be represented by an interval or a number of intervals on the real line. Example The solution to the inequality 2x+ 1 3 is the set of all x 1. 3 2.5 2 1.5 1 0.5 Ð 0.5 Ð 1 Ð 1 ...
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authentic way; that is, we don’t want to solve inequalities (Find all reals xso that 3x+2 >5), but rather prove inequality statements that are generally true. To illuminate this point, consider the simplest inequality: for all real x, x2 0: This statement is always true, and we can use it in clever ways to prove more general facts. Example.
