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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Equations with Radicals and Exponents

## Raising Each Side to a Power

Example 1

Raising each side to a power to eliminate radicals

Solve each equation.

a)

b)

 a) Original equation Cube each side. 3x + 5 = x - 1 2x = -6 x = -3

Check x = -3 in the original equation:

Note that is a real number. The solution set is {-3}. In this example we checked for arithmetic mistakes. There was no possibility of extraneous solutions here because we raised each side to an odd power.

 b) = x Original equation 3x + 18 = x2 Square both sides. -x2 + 3x + 18 = x2 Simplify. x2 - 3x - 18 = 0 Subtract x2 from each side to get zero on one side. (x - 6)(x + 3) = 0 Multiply each side by -1 for easier factoring. x - 6 = 0 Factor. x = 0 or x + 3 = 0 Zero factor property = 6 or x = -3

Because we squared both sides, we must check for extraneous solutions. If x = -3 in the original equation , we get

which is not correct. If x = 6 in the original equation, we get which is correct. The solution set is {6}.