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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.
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 ...
Solve the inequality to Jind the possible range of values for x. List the possible values of y.
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.
Solving Linear Inequalities – Practice Questions. 1. Solve the following inequalities and present your answer in a number line: a) 2𝑥𝑥+ 1 ≥5 + 𝑥𝑥. b) 2(𝑥𝑥+ 2) < −14 −𝑥𝑥. c) 𝑥𝑥−6 ≥4𝑥𝑥+ 3. d) −4(𝑥𝑥−5) ≤−3(2𝑥𝑥−7) 2. Solve the following inequalities. List the integers in each ...
In this unit inequalities are solved by using algebra and by using graphs. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. 1. Introduction. arrowhead. It is an example of an inequality.
Absolute value inequalities can be solved using the basic concept underlying the property of absolute value equalities. Whereas the equation asks for all numbers
