Question 1

Solve the linear equation: $$-7x - 2 - 2(x + 1) = 7x + 3. $$What is the value of $$x$$?

Accepted Answer

$$x = -\frac{7}{16}$$

Question 2

Which of the following best describes the equation $$-5(x + 4) + 29 = 2x - 7(x + 1)$$?

Accepted Answer

Inconsistent equation

Question 3

Solve the quadratic equation by factoring: $$x^2 + 2x - 24 = 0$. What are the solutions?

Accepted Answer

$$x = -6,\ 4$$

Question 4

Claire has received scores of 85, 88, 87, and 80 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 82?

Accepted Answer

At least $$70$$

Question 5

Solve the equation using the quadratic formula: $$3x^2 + 10x + 4 = 0$. What are the solutions?

Accepted Answer

$$x = -5 - \frac{\sqrt{13}}{3},\ x = -5 + \frac{\sqrt{13}}{3}$$

Question 6

Solve and check the linear equation: $$6x + 6 = -10 + 9x. $$What is the value of $$x$$?

Accepted Answer

$$x = 16/3$$

Question 7

Solve the equation: $$\frac{9x}{8} - x = \frac{x}{40} - 4/5. $$What is the value of $$x$$?

Accepted Answer

$$x = -8$$

Question 8

For the equation $$\frac{2}{x} + 1 = \frac{5}{2x + 13}$$, which value(s) make the denominator(s) zero, and what is the solution?

Accepted Answer

Denominator zero at $$x = 0$$; solution $$x = -2/9$$

Question 9

Solve the equation by the square root property: $$4x^2 + 5 = 201$. What are the solutions?

Accepted Answer

$$x = -7,\ 7$$

Question 10

Solve the equation: $$(2x + 4)^2$ = 36. $$What are the solutions?

Accepted Answer

$$x = -5,\ 1$$

Question 11

Determine whether the equation $$27x + 13(x + 1) = 40(x + 1) - 27 is an $$identity, a conditional equation, or an inconsistent equation.

Accepted Answer

Identity

Question 12

Solve the linear inequality: $$24x + 12 \leq 4(5x - 4). $$Express the solution in interval notation.

Accepted Answer

$$(-\infty,\ -7]$$

Question 13

Solve the linear inequality: $$12x + 2 \u003e 2(5x - 5). $$Express the solution in interval notation.

Accepted Answer

$$(-6,\ \infty)$$

Question 14

Solve the rational equation: $$\frac{16}{8x - 8} + 1 = \frac{8}{2x - 1}. $$What value(s) make the denominator(s) zero, and what is the solution?

Accepted Answer

Denominator zero at $$x = 1$$; no solution ($$\emptyset)$$

Question 15

Solve the equation: $$\frac{1}{y + 3} - \frac{5}{y - 3} = \frac{2}{y^2$ - 9}. $$What is the solution?

Accepted Answer

$$y = -5$$

Question 16

Solve the equation: $$\frac{x}{2x + 2} = -2x + \frac{4x + 4 + 2x - 3}{x + 1}. $$What is the solution?

Accepted Answer

$$x = 3$$

Question 17

Solve the linear inequality: $$\frac{x - 2}{8} \geq \frac{x - 2}{12} + \frac{1}{24}. $$Express the solution in interval notation.

Accepted Answer

$$[3,\ \infty)$$

College Algebra Unit 1 Review: Step-by-Step Guidance

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