,MATH101/MATH 101 Module Exam 2 | College Algebra
| Portage Learning | Q & A | 2026 Edition (PDF)
1. Which of the following best describes the solution set for the linear equation \(2(3x - 4) = 8x + 6\)?
A) \(x = -7\)
B) \(x = -1\)
C) \(x = 1\)
D) \(x = 7\)
Correct Answer: \(x = -7\)
Rationale: Distribute on the left side: \(6x - 8 = 8x + 6\). Subtract \(6x\) from both sides: \(-8 = 2x + 6\).
Subtract 6 from both sides: \(-14 = 2x\). Divide by 2: \(x = -7\).
2. What is the solution to the linear equation \(5 - 2(x + 3) = 4x - 7\)?
A) \(x = 1\)
B) \(x = -1\)
C) \(x = 2\)
D) \(x = 0\)
Correct Answer: \(x = 1\)
Rationale: Distribute: \(5 - 2x - 6 = 4x - 7\). Combine like terms: \(-1 - 2x = 4x - 7\). Add \(2x\) to both
sides: \(-1 = 6x - 7\). Add 7: \(6 = 6x\). Divide by 6: \(x = 1\).
3. A number, when decreased by 12 and then multiplied by 4, equals 80. What is the number?
A) 17
B) 20
C) 32
D) 38
,Correct Answer: 32
Rationale: Translate the problem into an equation: \(4(x - 12) = 80\). Divide both sides by 4: \(x - 12 =
20\). Add 12 to both sides: \(x = 32\).
4. The sum of two consecutive even integers is 94. What is the smaller integer?
A) 44
B) 46
C) 48
D) 50
Correct Answer: 46
Rationale: Let the integers be \(x\) and \(x+2\). The equation is \(x + (x+2) = 94\). Simplify: \(2x + 2 =
94\). Subtract 2: \(2x = 92\). Divide by 2: \(x = 46\).
5. Which of the following correctly solves the formula \(A = P(1 + rt)\) for \(t\)?
A) \(t = \frac{A - P}{Pr}\)
B) \(t = \frac{A - 1}{Pr}\)
C) \(t = \frac{A}{P} - 1\)
D) \(t = \frac{A - P}{r}\)
Correct Answer: \(t = \frac{A - P}{Pr}\)
Rationale: Divide both sides by P: \(\frac{A}{P} = 1 + rt\). Subtract 1: \(\frac{A}{P} - 1 = rt\). Simplify the
left side: \(\frac{A - P}{P} = rt\). Divide by r: \(t = \frac{A - P}{Pr}\).
6. After a 15% discount, the price of a coat is \( \$255\). What was the original price?
A) \( \$225\)
, B) \( \$270\)
C) \( \$300\)
D) \( \$330\)
Correct Answer: \( \$300\)
Rationale: Let the original price be \(x\). The equation is \(x - 0.15x = 255\), or \(0.85x = 255\). Divide
both sides by 0.85: \(x = 300\).
7. What is the slope of the line passing through the points \((-2, 5)\) and \((4, -7)\)?
A) \(-2\)
B) \(-\frac{1}{2}\)
C) \(\frac{1}{2}\)
D) \(2\)
Correct Answer: \(-2\)
Rationale: Use the slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - 5}{4 - (-2)} = \frac{-12}{6} =
-2\).
8. Which equation represents the line with a slope of \(-\frac{2}{3}\) that passes through the point \((6,
1)\)?
A) \(y = -\frac{2}{3}x + 5\)
B) \(y = -\frac{2}{3}x - 3\)
C) \(y = -\frac{2}{3}x + 1\)
D) \(y = -\frac{2}{3}x + 6\)
Correct Answer: \(y = -\frac{2}{3}x + 5\)
| Portage Learning | Q & A | 2026 Edition (PDF)
1. Which of the following best describes the solution set for the linear equation \(2(3x - 4) = 8x + 6\)?
A) \(x = -7\)
B) \(x = -1\)
C) \(x = 1\)
D) \(x = 7\)
Correct Answer: \(x = -7\)
Rationale: Distribute on the left side: \(6x - 8 = 8x + 6\). Subtract \(6x\) from both sides: \(-8 = 2x + 6\).
Subtract 6 from both sides: \(-14 = 2x\). Divide by 2: \(x = -7\).
2. What is the solution to the linear equation \(5 - 2(x + 3) = 4x - 7\)?
A) \(x = 1\)
B) \(x = -1\)
C) \(x = 2\)
D) \(x = 0\)
Correct Answer: \(x = 1\)
Rationale: Distribute: \(5 - 2x - 6 = 4x - 7\). Combine like terms: \(-1 - 2x = 4x - 7\). Add \(2x\) to both
sides: \(-1 = 6x - 7\). Add 7: \(6 = 6x\). Divide by 6: \(x = 1\).
3. A number, when decreased by 12 and then multiplied by 4, equals 80. What is the number?
A) 17
B) 20
C) 32
D) 38
,Correct Answer: 32
Rationale: Translate the problem into an equation: \(4(x - 12) = 80\). Divide both sides by 4: \(x - 12 =
20\). Add 12 to both sides: \(x = 32\).
4. The sum of two consecutive even integers is 94. What is the smaller integer?
A) 44
B) 46
C) 48
D) 50
Correct Answer: 46
Rationale: Let the integers be \(x\) and \(x+2\). The equation is \(x + (x+2) = 94\). Simplify: \(2x + 2 =
94\). Subtract 2: \(2x = 92\). Divide by 2: \(x = 46\).
5. Which of the following correctly solves the formula \(A = P(1 + rt)\) for \(t\)?
A) \(t = \frac{A - P}{Pr}\)
B) \(t = \frac{A - 1}{Pr}\)
C) \(t = \frac{A}{P} - 1\)
D) \(t = \frac{A - P}{r}\)
Correct Answer: \(t = \frac{A - P}{Pr}\)
Rationale: Divide both sides by P: \(\frac{A}{P} = 1 + rt\). Subtract 1: \(\frac{A}{P} - 1 = rt\). Simplify the
left side: \(\frac{A - P}{P} = rt\). Divide by r: \(t = \frac{A - P}{Pr}\).
6. After a 15% discount, the price of a coat is \( \$255\). What was the original price?
A) \( \$225\)
, B) \( \$270\)
C) \( \$300\)
D) \( \$330\)
Correct Answer: \( \$300\)
Rationale: Let the original price be \(x\). The equation is \(x - 0.15x = 255\), or \(0.85x = 255\). Divide
both sides by 0.85: \(x = 300\).
7. What is the slope of the line passing through the points \((-2, 5)\) and \((4, -7)\)?
A) \(-2\)
B) \(-\frac{1}{2}\)
C) \(\frac{1}{2}\)
D) \(2\)
Correct Answer: \(-2\)
Rationale: Use the slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-7 - 5}{4 - (-2)} = \frac{-12}{6} =
-2\).
8. Which equation represents the line with a slope of \(-\frac{2}{3}\) that passes through the point \((6,
1)\)?
A) \(y = -\frac{2}{3}x + 5\)
B) \(y = -\frac{2}{3}x - 3\)
C) \(y = -\frac{2}{3}x + 1\)
D) \(y = -\frac{2}{3}x + 6\)
Correct Answer: \(y = -\frac{2}{3}x + 5\)
