Solving Rational Equations and Inequalities. Solve 4 3x - 5 = 4 4 (3x – 5) = 4 4 = 12x - 20 2 = x.

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Presentation transcript:

Solving Rational Equations and Inequalities

Solve 4 3x - 5 = 4 4 (3x – 5) = 4 4 = 12x = x

Solve x - 5 x 2 – 3x – 4 = 3x + 2 x 2 – 1 Factor the bases x - 5 (x – 4)(x + 1) = 3x + 2 (x – 1)(x + 1) reduce (x – 5)(x – 1) = (3x + 2)(x – 4) x 2 – 6x + 5 = 3x 2 – 10x – 8 2x 2 – 4x – 13 = 0 Use the QF to solve

If the resulting equation is a cubic or quartic, we could use the Factor Theorem or Technology to solve…

Solve (inequality) 2 x – 5 10 Better to write it equal to 0 2 x – – 10x + 50 x – 5 0 – 10x + 52 x – 5 0 – 10x + 52 x – 5 f(x) = Now consider DIVER, and graph

From the graph, all the points below the x axis satisfy the inequality f(x) < 0 For x 5.2

Practise Pg 183 1a,b,c (y = 0, solve for x) 2a,c,e 5a (use technology for now)