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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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Question 1: Lauren goes shopping and has £50 to spend. She bought a T-shirt and 3 pairs of leggings. The T-shirt cost £23. Each pair of leggings cost £x. Form an inequality in terms of x. Solve the inequality to Jind the possible price of the leggings. Question 2: Farmer Taylor is placing a fence around his Jield.
Solve each of the following inequalities. a) 2 + 2 ( 4 x + 3 ) ≥ 2 ( 2 x − 1 ) + 2 x. 8 + 3 ( x + 3 ) ≤ 2 ( 2 x + 1. ) c) 6 − 4 ( 4 − x ) > 4. 16 − 4 ( 7 + x ) ≤ 8. ≥ − 5.
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Inequalities which involve variables are called literal inequalities. For example, (iii) x > 3, y ≤ 5, x – y ≥ 0. An inequality may contain more than one variable and it can be linear, quadratic or cubic etc.
Oct 5, 2020 · An inequality is a set of points that can be represented on a number line. The inequality is either represented as an open circle or a closed circle. Looking at the illustration below, the following interpretations can be
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.
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Inequalities can be represented on a number line, as shown in the following worked examples. Worked Example 1 Represent the following inequalities on a number line. (a) x ≥2 (b) x <−1 (c) −<≤24x Solution (a) The inequality, x ≥2, states that x must be greater than or equal to 2. This is represented as shown. – 2 – 10 1 2 3 4 x
