Question 1

Evaluate the algebraic expression $$x^2 - 6x + 5$ for x = 7$.

Accepted Answer

$$6$$

Question 2

Write the expression $$- (6x - 9y - 6)$$ without parentheses.

Accepted Answer

$$-6x + 9y + 6$$

Question 3

Simplify the expression $$8(6y - 4) - (5y + 7). $$What is the result?

Accepted Answer

$$43y - 39$$

Question 4

Solve the linear equation $$9x - (5x - 6) = 26$$ for $$x.$$

Accepted Answer

$$x = 6$$

Question 5

A chemist is mixing two solutions. The first solution contains $$x$$ grams of salt, and the second contains $$2x - 5$$ grams. If the total salt is $$21$$ grams, what is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 6

Which of the following is the correct simplification of $$-3(2x - 4y + 5) + 7x$$?

Accepted Answer

$$x + 12y - 15$$

Question 7

A medical researcher is tracking the number of bacteria in a culture, modeled by $$N = 2t^2$ - 5t + 8$$, where $$t is $$time in hours. How many bacteria are present at $$t = 3$$ hours?

Accepted Answer

$$17$$

Question 8

Which of the following is equivalent to $$4(x - 2y) - 3(x + y)$$?

Accepted Answer

$$x - 11y$$

Question 9

A car rental company charges a base fee of $$b$$ dollars and $$0.25$$ dollars per mile driven. If the total cost for $$m$$ miles is $$C = b + 0.25m$$, what is the cost for $$b = 20$$ and $$m = 60$$?

Accepted Answer

$$35$$

Question 10

Which of the following is the correct solution to the equation $$2(x - 3) + 4 = 10$$?

Accepted Answer

$$x = 6$$

Question 11

A biologist models the population of a species as $$P = 5n^2$ - 2n + 7$$, where $$n is $$the number of years since observation began. What is the population at $$n = 2$$?

Accepted Answer

$$23$$

Question 12

Simplify the expression $$7(2x - 3) - 4(x + 5).$$

Accepted Answer

$$10x - 41$$

Question 13

A historical event occurred $$x$$ years ago. If the sum of the years since the event and twice that number is $$75$$, what is $$x$$?

Accepted Answer

$$25$$

Question 14

Which of the following is the correct simplification of $$-2(3x - 4y) + 5(x + 2y)$$?

Accepted Answer

$$-x + 18y$$

Question 15

A pharmaceutical company models the cost of producing $$x$$ units of a drug as $$C = 3x^2$ - 4x + 10. $$What is the cost for $$x = 2$$?

Accepted Answer

$$14$$

Question 16

Solve for $$x$$: $$5x - 2(x + 3) = 7.$$

Accepted Answer

$$x = 3$$

Question 17

A company’s profit is modeled by $$P = 4x - 7$$, where $$x is $$the number of products sold. If the profit is $$21$$, how many products were sold?

Accepted Answer

$$6$$

Question 18

Which of the following is the correct simplification of $$3(2x - 5y) - 2(4x + y)$$?

Accepted Answer

$$-2x - 17y$$

Question 19

A scientist records the temperature in degrees Celsius as $$T = 2x^2$ - 3x + 4$$, where $$x is $$the number of hours after midnight. What is the temperature at $$x = 3$$?

Accepted Answer

$$13$$

Question 20

Solve for $$x$$: $$7x - 4(x - 2) = 18.$$

Accepted Answer

$$x = 4$$

College Algebra: Algebraic Expressions and Linear Equations Study Guide

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