Question 1

Solve the equation $$2 + \frac{10}{x} = x + 5. $$What are the solutions?

Accepted Answer

$$x = -5,\ 2$$

Question 2

Solve the equation $$\frac{a}{a-6} = \frac{-5}{a-4}. $$What is the solution?

Accepted Answer

$$a = -6.5$$

Question 3

Solve the radical equation $$\sqrt{6x + 6} = 6. $$What is the solution set?

Accepted Answer

$$x = 5$$

Question 4

Solve the radical equation $$\sqrt{7 - 21x} = x + 9. $$What is the solution set?

Accepted Answer

$$x = -2$$

Question 5

What number must be added to $$x^2 + 12x$ to make it a perfect square trinomial?

Accepted Answer

$$36$$

Question 6

What number must be added to $$x^2 - 8x$ to make it a perfect square trinomial?

Accepted Answer

$$16$$

Question 7

Solve the equation $$x^2 + 6x - 4 = 0$ using the quadratic formula.

Accepted Answer

$$x = -3 \pm \sqrt{13}$$

Question 8

Solve the quadratic equation $$2x^2 - 2x + 7 = 0$ using the quadratic formula.

Accepted Answer

$$x = \frac{1 \pm \sqrt{15}}{2}$$

Question 9

Multiply both sides of the equation $$\frac{7x}{3} + 4 = \frac{1}{6} by 6. $$What is the resulting equation?

Accepted Answer

$$14x + 24 = 1$$

Question 10

Solve the equation $$\frac{6y}{y-8} + 2 = \frac{4y}{y-8}. $$What is the solution?

Accepted Answer

$$y = 4$$

Question 11

Solve the equation $$b^2 - 5b = 36$ by factoring.

Accepted Answer

$$b = 9,\ -4$$

Question 12

Solve the equation $$3x^2 + 7x - 6 = 0$ by factoring.

Accepted Answer

$$x = \frac{2}{3},\ -3$$

Question 13

Solve the equation $$9x^2 - 4 = 9x$ by factoring.

Accepted Answer

$$x = \frac{1}{3},\ \frac{4}{3}$$

Question 14

Find the sum $$(8 - 2i) + (3 + 5i)$$ and write the answer in the form $$a + bi.$$

Accepted Answer

$$11 + 3i$$

Question 15

Multiply $$(9 - 9i)(7 - 4i)$$ and write the answer in the form $$a + bi.$$

Accepted Answer

$$27 - 99i$$

Question 16

Solve by using the square root property: $$(x - 7)^2$ = 36. $$What are the solutions?

Accepted Answer

$$x = 13,\ 1$$

Question 17

Solve $$8y + 2(y - 4) = 5(y + 1) - 2. $$What is the solution?

Accepted Answer

$$y = 11/5$$

Question 18

Solve the equation $$6(7x + 9) = 42x + 54. $$What is the solution?

Accepted Answer

The solution is all real numbers.

Question 19

Solve the equation $$3n^2 + 27n = 0$ by factoring.

Accepted Answer

$$n = 0,\ -9$$

Question 20

Solve $$5 - 4(x + 4) = 6x - 31. $$What is the solution?

Accepted Answer

$$x = 2$$

Question 21

Determine whether the equation $$9x^2 + 3x = 33$ is linear or non-linear.

Accepted Answer

The equation is non-linear.

Precalculus Equation Solving and Algebraic Techniques Study Guide

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