2.8 - Solving Equations in One Variable

By the end of today you should be able to…….

•Solve Rational Equations•Eliminate Extraneous solutions•Solve Polynomial Inequalities•Solve Rational & other Inequalities

Solving Rational Equations• Rational Equations: equations involving rational

expressions or fractions and can be written in the form of:

f(x)g(x)

where f(x) and g(x) are polynomial functions with no common factors and the zeros of f(x) are the solutions of the equations.

• Extraneous Solutions: Not solutions of the original equations.

= 0

You Try! Solve the equation algebraically. Check for extraneous solutions. Support your answers numerically

x + 2 = 15

x

Solve Algebraically: Support Numerically:

x + 4x = 12 x - 3 x - 3

Solve the equation algebraically. Check for extraneous solutions. Support your answers numerically

Solve Algebraically:

Check Numerically:

Solve the equation graphically. Confirm your answer algebraically and identify extraneous solutions

2 - 1 = 1 x + 1 x2 +

xSolve Graphically:

Check Algebraically:

Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically.

x – 3 - 3 + 3 = 0

x x + 1 x2 + xCheck Graphically:Solve Algebraically:

2.9 – Solving Inequalities in One Variable

Polynomial Inequalities

•To solve the inequality f(x) > 0 is to find the values of x that make f(x) positive

x + 5 > 0

•To solve the inequality f(x) < 0 is to find values of x that make f(x) negative

x + 5 < 0

Where is the polynomial zero, positive, or negative?

f(x) = (x + 2)(x + 1)(x – 5)

a) x values that cause f(x) to be zero?

b) x values that cause f(x) to be positive?

c) x values that cause f(x) to be negative?

Solve the polynomial inequality graphically:

x3 – x2 – 2x ≥ 0

Solve graphically: Check:

Solve the inequality: x3 (x – 2) (x + 3)2

< 0

You Try! Complete the factoring if needed, and solve the polynomial inequality using a sign chart.

(x + 1)(x - 3)2 > 0

You Try! Solve the equation graphically. Confirm your answer algebraically and identify extraneous solutions

x + 6 = -7 x

You Try! Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically.

4x + 3 = 15x + 4 x – 1 x2 + 3x

-4

Don’t Forget your Homework!

Pg. 254-256 (#4-32 every 4)

Pg. 265 – 266 (#4-50 every 4)