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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.
Question 1: Solve each of the inequalities below (a) (b) (c) (d) (e) (f) (g) (h) Question 2: Solve each of the inequalities below (a) (b) (c) (d) (e) (f) (g) (h) Question 3: Solve each inequality below and represent the solution on a number line. (a) (b) (c) (d)
To solve our inequality we need to find the values of x for which the hyperbola lies on or under the line y =1.(5,1) is the point of intersection. So, from the graph we see that 1 x−4 ≤ 1 when x<4orx ≥ 5. 4. Solve x−3 < 10 x. Consider x−3=10 x, x =0. Multiply by x we get x2 −3x =10 x2 −3x−10 = 0 (x−5)(x+2) = 0 Therefore, the ...
Use a graphing calculator to solve (a) 2x − 1 < x + 2 and (b) 2x − 1 ≤ x + 2. SOLUTION a. Enter the inequality 2x − 1 < x + 2 into a graphing calculator. Press graph. Y1=2X-1<X+2 Y2= Y3= Y4= Y5= Y6= Y7= Use the inequality symbol <. −4 −3 3 4 x < 3 x = 3 The solution of the inequality is x < 3. b.
In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization prob- lems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad.
Compiled by Navan Mudali Page 23 of 83 February 2011 QUESTION 1 1.1 Solve for x, correct to TWO decimal places, where necessary: 1.1.1 x(x 1) 12 (3) 1.1.2 2x2 3x 7 0 (4) 1.1.3 7x2 18x 9 ! 0 (4) 1.2 Solve for x and y simultaneously: 2x y 7 x2 xy 21 y2 (7) 1.3 Simplify completely, without the use of a calculator:
Solving inequalities is the same as solving equations. There are only 2 things you need to know... ¡ 1.) If you multiply or divide by a negative number you must switch the sign. negative means switch the sign!! ¡ 2.) You will graph your solutions. When solving inequalities, if you multiply or divide by a negative you must switch the signs.
