Pre-calculus Algebra Exam Questions with Verified Solutions (Graded A+)
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|3x + 5| = 7 - Answers 2/3,-4
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|7x| = 2 - Answers 2/7, -2/7
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|x − 6| = 0.01 - Answers 6.04, 5.99
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|x − 8| = −10 - Answers no solution
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|−4x| = 19 - Answers -19/4, 19/4
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
12
|x| − 1 = 4 - Answers 10, -10
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|x − 8| = −5 - Answers No Solution
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
15 + |2x − 5| = 12 - Answers No solution
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|x − 8| = |3x + 9| - Answers -17/2, -1/4
, Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|x + 3| = |2x + 2| - Answers 1, -5/3
Solve the inequality. Express the answer using interval notation.
|3x| ≤ 18 - Answers [-6, 6]
Solve the inequality. Express the answer using interval notation.
12
|x| ≥ 3 - Answers (-00, -3)U(9, 00)
Solve the inequality. Express the answer using interval notation.
|x + 1| ≤ 0 - Answers the point x = −1
Solve the inequality. Express the answer using interval notation.
|3x − 2| > 10 - Answers (-00, -8/3)U(4, 00)
Solve the inequality. Express the answer using interval notation.
|5x − 8| < 10 - Answers (-2/5, 18/5)
Solve the inequality. Express the answer using interval notation.
7|x + 3| + 8 > 2 - Answers (-00, 00)
Yes or No? If No, give a reason.
(a) Is the expression (x + 6)2 equal to x2 + 36?
(b) When you expand
(x + a)2,
where
a ≠ 0,
do you get three terms? - Answers No, it is equal to x2 + 12x + 36.
Yes, you get three terms.
Find the sum, difference, or product. (Simplify your answer completely.)
6(x − 7) + 8(x + 2) - Answers 14x-26
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|3x + 5| = 7 - Answers 2/3,-4
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|7x| = 2 - Answers 2/7, -2/7
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|x − 6| = 0.01 - Answers 6.04, 5.99
Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real
solution, enter NO REAL SOLUTION.)
|x − 8| = −10 - Answers no solution
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|−4x| = 19 - Answers -19/4, 19/4
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
12
|x| − 1 = 4 - Answers 10, -10
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|x − 8| = −5 - Answers No Solution
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
15 + |2x − 5| = 12 - Answers No solution
Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|x − 8| = |3x + 9| - Answers -17/2, -1/4
, Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO
SOLUTION.)
|x + 3| = |2x + 2| - Answers 1, -5/3
Solve the inequality. Express the answer using interval notation.
|3x| ≤ 18 - Answers [-6, 6]
Solve the inequality. Express the answer using interval notation.
12
|x| ≥ 3 - Answers (-00, -3)U(9, 00)
Solve the inequality. Express the answer using interval notation.
|x + 1| ≤ 0 - Answers the point x = −1
Solve the inequality. Express the answer using interval notation.
|3x − 2| > 10 - Answers (-00, -8/3)U(4, 00)
Solve the inequality. Express the answer using interval notation.
|5x − 8| < 10 - Answers (-2/5, 18/5)
Solve the inequality. Express the answer using interval notation.
7|x + 3| + 8 > 2 - Answers (-00, 00)
Yes or No? If No, give a reason.
(a) Is the expression (x + 6)2 equal to x2 + 36?
(b) When you expand
(x + a)2,
where
a ≠ 0,
do you get three terms? - Answers No, it is equal to x2 + 12x + 36.
Yes, you get three terms.
Find the sum, difference, or product. (Simplify your answer completely.)
6(x − 7) + 8(x + 2) - Answers 14x-26
