Question 1

Solve for $$x$$: $$2(x^2 + 11) = 3x + 22$

Accepted Answer

$$x = 3, x = -rac{11}{2}$$

Question 2

Which of the following is the correct solution to $$x^2 + 5x$$ = $$2x^2 + 25x$?

Accepted Answer

$$x = 0, x = -20$$

Question 3

What is the solution to $$|2x| = 4$$?

Accepted Answer

$$x = 2, x = -2$$

Question 4

Given the equation $$4(x-2) - \frac{3}{x-3} = 5$$, which of the following is a solution?

Accepted Answer

$$x = 2$$

Question 5

Which of the following best describes the solution set for $$|2x| = 4$$?

Accepted Answer

Two real solutions

Question 6

If $$x^2 + 5x$$ = $$2x^2 + 25x$, what is the value of x$ after rearranging and factoring?

Accepted Answer

$$x = 0 or$$ $$x = -20$$

Question 7

Which of the following is the correct first step to solve $$2(x^2 + 11) = 3x + 22$?

Accepted Answer

Expand to $$2x^2 + 22 = 3x + 22$

Question 8

What is the correct way to isolate $$x in$$ $$|2x| = 4$$?

Accepted Answer

Set $$2x = 4$$ and $$2x = -4$$

Question 9

In the equation $$4(x-2) - \frac{3}{x-3} = 5$$, what is the restriction on $$x$$?

Accepted Answer

$$x 
eq 3$$

Question 10

After solving $$4(x-2) - \frac{3}{x-3} = 5$$, which quadratic equation do you obtain?

Accepted Answer

$$4x^2 - 5x - 6 = 0$

Question 11

Which of the following is a valid solution to $$4x^2 - 5x - 6 = 0$?

Accepted Answer

$$x = 2$$

Question 12

If you solve $$2(x^2 + 11) = 3x + 22$ and get x^2$ - 3x - 11 = 0$$, what is the next step?

Accepted Answer

Use the quadratic formula

Question 13

What is the discriminant of the quadratic $$x^2 - 3x - 11 = 0$?

Accepted Answer

$$D = (-3)^2$ - 4(1)(-11) = 9 + 44 = 53$$

Question 14

Which of the following is the correct solution for $$x in$$ $$x^2 - 3x - 11 = 0$ using the quadratic formula?

Accepted Answer

$$x = \frac{3 \pm \sqrt{53}}{2}$$

Question 15

If $$x^2 + 5x$$ = $$2x^2 + 25x$, what is the sum of all solutions?

Accepted Answer

$$-20$$

Question 16

Which of the following equations is equivalent to $$4(x-2) - \frac{3}{x-3} = 5$$ after multiplying both sides by $$(x-3)$$?

Accepted Answer

$$4(x-2)(x-3) - 3 = 5(x-3)$$

Question 17

What is the value of $$x$$ that makes $$|2x| = 4$$ true and is positive?

Accepted Answer

$$x = 2$$

Question 18

If $$x^2 - 3x - 11 = 0$, which of the following is the sum of the roots?

Accepted Answer

$$3$$

Question 19

Which of the following is a necessary step when solving $$4(x-2) - \frac{3}{x-3} = 5$$ for $$x$$?

Accepted Answer

Multiply both sides by $$(x-3) to $$clear the fraction

Solving Linear and Rational Equations: Precalculus Study Notes

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