Equations with fractions can be simplified by multiplying both sides by a common denominator. 3x + 4 = 2x + 8 3x = 2x + 4 x = 4 Example: Solve. 4 4 66.

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Presentation transcript:

Equations with fractions can be simplified by multiplying both sides by a common denominator. 3x + 4 = 2x + 8 3x = 2x + 4 x = 4 Example: Solve

Solving Proportions A proportion is an equation where two fractions are equal. We can solve by cross multiplying 5w + 10 = 7w = 2w – 7 17 = 2w

Find x- and y-intercepts Graph y = 16 – 3x Graph y = 16 – 3x Find x- and y – intercepts from graph Find x- and y – intercepts from graph Find x- and y – intercepts algebraically Let x = 0, y = 16 – 3(0) y = 16, y-intercept is (0, 16) Let y = 0, 0 = 16 – 3x 3x = 16 X = 16/3 x-intercept (16/3, 0)

x = does not work this is an extraneous solution, makes denominator of second fraction = 0 Extraneous solution When multiplying or dividing by a variable quantity, you may get an extraneous solution. When multiplying or dividing by a variable quantity, you may get an extraneous solution. An extraneous solution is a solution that does not satisfy the original equation. An extraneous solution is a solution that does not satisfy the original equation.

Solve for x in literal equation 6x + ax = 2x + 5 6x + ax = 2x + 5 4x + ax = 5subtract 2x 4x + ax = 5subtract 2x x(4 + a) = 5factor x(4 + a) = 5factor