Question 1

Solve the linear equation for $$x$$:

$$86 = 9x - 4$$

Accepted Answer

Question 2

Solve for $$x in $$the equation:

$$(-3x - 9) + 6 = -2(x - 1)$$

Accepted Answer

$$x = 1$$

Question 3

Simplify the following expression and write your answer in the form $$a+bi$$:

$$(7 + 6i)(5 - 7i)$$

Accepted Answer

$$35 - 49i + 30i - 42i^2$ = 77 - 19i$$

Question 4

Factor the polynomial:

$$25x^2 - 81$

Accepted Answer

$$(5x + 9)(5x - 9)$$

Question 5

Factor the quadratic polynomial:

$$5x^2 - 28x + 32$

Accepted Answer

$$(5x - 8)(x - 4)$$

Question 6

Factor the following perfect square trinomial:

$$x^2 + 50x + 625$

Accepted Answer

$$(x + 25)^2$

Question 7

Solve the quadratic equation by factoring:

$$x^2 = x + 20$

Accepted Answer

$$x = 5, x = -4$$

Question 8

Solve the quadratic equation using the square root property:

$$4x^2 = 60$

Accepted Answer

$$x = \pm\sqrt{15}$$

Question 9

Use the quadratic formula to solve the equation:

$$x^2 - 12x + 85 = 0$

Accepted Answer

$$x = 5, x = 17$$

Question 10

Solve the rational equation and state the values of $$x$$ that make the denominators zero:

$$\dfrac{4}{x - 2} = 1 + \dfrac{6}{x + 2}$$

Accepted Answer

The solution is $$x = 0$$, and the denominators are zero at $$x = 2$$ and $$x = -2$$

Question 11

Solve the radical equation and check all proposed solutions:

$$\sqrt{6x + 55} = x$$

Accepted Answer

The solution is $$x = 11$$, and it checks in the original equation.

Question 12

Solve the absolute value equation or indicate that the equation has no solution:

$$|5x + 6| + 7 = 11$$

Accepted Answer

$$x = 0.8$$ and $$x = -2$$

Question 13

Solve the linear inequality and express the solution in interval notation:

$$-6x + 4 \geq -7x - 1$$

Accepted Answer

$$[ -5, \infty )$$

Question 14

Solve the absolute value inequality and express the solution in interval notation:

$$|x - 5| - 9 \leq -1$$

Accepted Answer

$$[3, 7]$$

Question 15

Divide and write your answer in the form $$a+bi$$:

$$\dfrac{i}{9 + i}$$

Accepted Answer

$$\dfrac{9}{82} + \dfrac{1}{82}i$$

Question 16

A chemical solution is modeled by the equation $$C = 9x - 4$$, where $$C is $$the concentration in mg/L and $$x is $$the number of hours since mixing. If the concentration reaches $$86 mg/L$$, how many hours have passed?

Accepted Answer

$$x = 10$$

Question 17

A projectile's height in meters is given by $$h = -5t^2$ + 20t + 15. At $$what time $$t$$ does the projectile reach a height of $$35$$ meters? (Round to the nearest tenth if necessary.)

Accepted Answer

$$t = 1 or$$ $$t = 3$$

Question 18

A business's profit $$P (in $$thousands of dollars) is modeled by $$P = 5x^2$ - 28x + 32$$, where $$x is $$the number of units sold (in thousands). For what values of $$x$$ does the business break even (i.e., $$P = 0$$)?

Accepted Answer

Question 19

A medical test result is modeled by the equation $$\sqrt{6x + 55} = x$$, where $$x is $$the number of days since exposure. What is the earliest day the test will be positive?

Accepted Answer

$$x = 11$$

College Algebra Exam 1: Step-by-Step Study Guidance

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