このフィルターに一致する問題はありません。
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If 2x + 4 = 14, what is x?
- 3
- 4
- 5 ✓
- 6
解説
Subtract 4 from both sides: 2x = 10. Divide by 2: x = 5.
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If x/3 − 2 = 4, what is x?
- 6
- 12
- 18 ✓
- 24
解説
Add 2 to both sides: x/3 = 6. Multiply by 3: x = 18.
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If 5(x − 2) = 3x + 8, what is x?
- 7
- 8
- 9 ✓
- 10
解説
Distribute: 5x − 10 = 3x + 8. Subtract 3x: 2x − 10 = 8. Add 10: 2x = 18. Divide by 2: x = 9.
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If (3x − 1)/2 = (x + 5)/2, what is x?
- 2
- 3 ✓
- 4
- 5
解説
Both sides have the same denominator, so 3x − 1 = x + 5. Subtract x: 2x − 1 = 5. Add 1: 2x = 6. Divide: x = 3.
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If 3(x + 2) − 5(x − 1) = 2x + 7, what is x?
- 0
- 1 ✓
- 2
- 3
解説
Distribute: 3x + 6 − 5x + 5 = 2x + 7 → −2x + 11 = 2x + 7 → 4 = 4x → x = 1.
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What value of x satisfies 4x = 20?
- 4
- 5 ✓
- 6
- 8
解説
Divide both sides by 4: x = 5.
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If 7 − 3x = −11, what is x?
- 3
- 4
- 5
- 6 ✓
解説
Subtract 7 from both sides: −3x = −18. Divide by −3: x = 6.
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For the equation kx + 6 = 3x − 2, where k is a constant, the equation has no solution. What is k?
- 1
- 2
- 3 ✓
- 6
解説
For no solution, the coefficients of x must be equal but the constants different. Setting k = 3 gives 3x + 6 = 3x − 2, which simplifies to 6 = −2 — a contradiction. So k = 3.
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A line has slope 3 and passes through (0, −2). Which equation represents this line?
- y = 3x + 2
- y = −3x + 2
- y = 3x − 2 ✓
- y = −2x + 3
解説
Slope-intercept form: y = mx + b with m = 3 and b = −2 gives y = 3x − 2.
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What is the slope of the line 2x − 4y = 8?
- 2
- −2
- 1/2 ✓
- −1/2
解説
Solve for y: −4y = −2x + 8 → y = (1/2)x − 2. The slope is 1/2.
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A line passes through (2, 5) and (6, 13). What is the y-intercept?
- −1
- 0
- 1 ✓
- 2
解説
Slope = (13 − 5)/(6 − 2) = 2. Using y = 2x + b and point (2, 5): 5 = 4 + b → b = 1.
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Which equation represents a line perpendicular to y = 3x + 5?
- y = 3x − 2
- y = −3x + 1
- y = (1/3)x + 2
- y = −(1/3)x + 4 ✓
解説
Perpendicular lines have slopes that are negative reciprocals. The slope of y = 3x + 5 is 3, so the perpendicular slope is −1/3. Only y = −(1/3)x + 4 has this slope.
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Line L passes through (1, 4) and is parallel to 3x + 2y = 6. What is the equation of L?
- y = −(3/2)x + 11/2 ✓
- y = (3/2)x + 5/2
- y = −(2/3)x + 14/3
- y = −(3/2)x + 4
解説
3x + 2y = 6 → y = −(3/2)x + 3, so slope = −3/2. L: y − 4 = −(3/2)(x − 1) → y = −(3/2)x + 3/2 + 4 = −(3/2)x + 11/2.
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A cab company charges a flat fee of $3.00 plus $1.50 per mile. If the total fare is $15.00, how many miles was the trip?
- 6
- 7
- 8 ✓
- 9
解説
3 + 1.5m = 15 → 1.5m = 12 → m = 8 miles.
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What is the x-intercept of the line y = 2x − 6?
- 2
- 3 ✓
- 6
- −6
解説
Set y = 0: 0 = 2x − 6 → 2x = 6 → x = 3.
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In the equation y = ax + b, increasing x by 4 increases y by 10. What is a?
- 2
- 5/2 ✓
- 2/5
- 5
解説
The slope a = Δy/Δx = 10/4 = 5/2.
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If x + y = 8 and x − y = 2, what is x?
- 3
- 4
- 5 ✓
- 6
解説
Add the equations: 2x = 10 → x = 5.
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Given 2x + y = 7 and x − y = 2, what is x + y?
- 3
- 4 ✓
- 5
- 6
解説
Add equations: 3x = 9 → x = 3. From x − y = 2: y = 1. So x + y = 4.
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Given 3x + 2y = 16 and x − y = 2, what is y?
- 1
- 2 ✓
- 3
- 4
解説
From x − y = 2: x = y + 2. Substitute: 3(y + 2) + 2y = 16 → 5y + 6 = 16 → 5y = 10 → y = 2.
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How many solutions does the system 5x + 3y = 11 and 10x + 6y = 22 have?
- 0
- 1
- 2
- Infinitely many ✓
解説
The second equation is exactly 2 times the first, so they represent the same line. Every point on the line is a solution — infinitely many.
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The system ax + 2y = 6 and 3x + y = 4 has no solution. What is a?
- 2
- 4
- 6 ✓
- 8
解説
For no solution, coefficient ratios must match but constants must not: a/3 = 2/1 → a = 6. Check: 6/3 = 2 = 2/1, but 6 ≠ 2 × 4 = 8. Confirmed no solution.
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A store sells apples for $0.50 each and bananas for $0.30 each. Maria buys 20 pieces of fruit for $8.00. How many apples did she buy?
- 8
- 9
- 10 ✓
- 12
解説
Let a = apples, b = bananas. a + b = 20 and 0.5a + 0.3b = 8. Substituting b = 20 − a: 0.5a + 0.3(20 − a) = 8 → 0.2a = 2 → a = 10.
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If y = 2x + 1 and y = 5, what is x?
- 1
- 2 ✓
- 3
- 4
解説
Substitute y = 5: 2x + 1 = 5 → 2x = 4 → x = 2.
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Two numbers have a sum of 24 and a difference of 8. What is their product?
- 112
- 120
- 128 ✓
- 136
解説
x + y = 24 and x − y = 8. Adding: 2x = 32 → x = 16, y = 8. Product = 16 × 8 = 128.
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Which values of x satisfy 3x − 6 > 9?
- x > 2
- x > 3
- x > 5 ✓
- x > 7
解説
Add 6: 3x > 15. Divide by 3: x > 5.
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Which values of x satisfy −2x + 4 ≤ 10?
- x ≤ −3
- x ≥ −3 ✓
- x ≤ 3
- x ≥ 3
解説
Subtract 4: −2x ≤ 6. Divide by −2 (flip the inequality): x ≥ −3.
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A student needs an average of at least 80 to pass a two-test course. She scored 65 on the first test. What is the minimum score she needs on the second test?
- 85
- 90
- 95 ✓
- 100
解説
(65 + x)/2 ≥ 80 → 65 + x ≥ 160 → x ≥ 95.
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What is the solution set for |2x − 4| < 6?
- −1 < x < 5 ✓
- −5 < x < 1
- x < −1 or x > 5
- x < 1 or x > −5
解説
−6 < 2x − 4 < 6 → −2 < 2x < 10 → −1 < x < 5.
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Which of the following is NOT a solution to 4 − x > 2?
- −1
- 0
- 1
- 2 ✓
解説
4 − x > 2 → −x > −2 → x < 2. So x = 2 is NOT a solution (it makes the inequality false).
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Which inequality represents "all real numbers less than or equal to 3"?
- x < 3
- x > 3
- x ≥ 3
- x ≤ 3 ✓
解説
"Less than or equal to 3" is written x ≤ 3.
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The inequality 3(x + 2) ≤ 2(x + 5) is equivalent to which of the following?
- x ≤ 2
- x ≤ 4 ✓
- x ≥ 4
- x ≤ 8
解説
3x + 6 ≤ 2x + 10 → x ≤ 4.
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A company's profit P (in dollars) satisfies P = 50n − 200, where n is items sold. What is the minimum number of items the company must sell to make a profit?
- 3
- 4
- 5 ✓
- 6
解説
50n − 200 > 0 → n > 4. The smallest integer greater than 4 is 5.
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The function C(x) = 3x + 7 gives the cost (in dollars) of renting a bicycle for x hours. What does the 7 represent?
- The hourly rate
- The total cost
- The initial flat fee ✓
- The number of hours
解説
In y = mx + b, b is the y-intercept — the value when x = 0. Here, 7 is the cost before any hours are added, so it is the initial flat fee.
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A table shows (1, 5), (2, 8), (3, 11), (4, 14). What is the rate of change?
- 2
- 3 ✓
- 4
- 5
解説
Rate of change = (8 − 5)/(2 − 1) = 3. This holds for every consecutive pair in the table.
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A linear model predicts a town's population grows by 450 people per year. The population was 12,000 in 2020. What does the model predict for 2025?
- 13,500
- 14,000
- 14,250 ✓
- 15,000
解説
2025 is 5 years after 2020. 12,000 + 5 × 450 = 12,000 + 2,250 = 14,250.
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Line ℓ: y = 2x passes through the origin. Line m is perpendicular to ℓ and passes through (4, 0). What are the coordinates of their intersection?
- (4/5, 8/5) ✓
- (1, 2)
- (2, 4)
- (8/5, 4/5)
解説
Slope of m = −1/2. m: y = −(1/2)(x − 4). Set equal to ℓ: 2x = −x/2 + 2 → 5x/2 = 2 → x = 4/5, y = 8/5.
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If f(x) = −2x + 10, for what value of x does f(x) = 0?
- 2
- 3
- 5 ✓
- 10
解説
−2x + 10 = 0 → −2x = −10 → x = 5.
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A phone plan charges $30 per month plus $0.10 per text message. Which equation gives the monthly cost C for t text messages?
- C = 0.10t
- C = 30t
- C = 30 + 0.10t ✓
- C = 30t + 0.10
解説
Fixed cost ($30) plus variable cost ($0.10 per text) gives C = 30 + 0.10t.
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f and g are linear functions with the same slope. f(2) = 5, f(6) = 13, and g(0) = 7. What is g(3)?
- 11
- 12
- 13 ✓
- 14
解説
Slope of f = (13 − 5)/(6 − 2) = 2. g(x) = 2x + 7 (since g(0) = 7). g(3) = 6 + 7 = 13.
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In the model y = −3x + 24, y represents remaining pages and x represents hours of reading. What is the total number of pages in the book?
- 3
- 8
- 21
- 24 ✓
解説
When x = 0 (no reading yet), y = 24. That is the total page count.
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If 6x − 3 = 21, what is x?
- 2
- 3
- 4 ✓
- 5
解説
Add 3 to both sides: 6x = 24. Divide by 6: x = 4.
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What is the value of x if 2(x + 5) = 18?
- 3
- 4 ✓
- 5
- 6
解説
Distribute: 2x + 10 = 18 → 2x = 8 → x = 4.
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Which equation represents a line with slope −2 and y-intercept 5?
- y = 2x + 5
- y = −2x − 5
- y = −2x + 5 ✓
- y = 5x − 2
解説
Slope-intercept form y = mx + b: m = −2 and b = 5 gives y = −2x + 5.
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If y = 4 when x = 0, and y increases by 3 for every increase of 1 in x, which equation models this?
- y = 4x + 3
- y = 3x − 4
- y = 3x + 4 ✓
- y = −3x + 4
解説
y-intercept = 4, slope = 3. Slope-intercept form: y = 3x + 4.
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If 4(2x − 1) = 3(x + 7), what is x?
- 3
- 4
- 5 ✓
- 6
解説
Distribute: 8x − 4 = 3x + 21 → 5x = 25 → x = 5.
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Which values of x satisfy 5x + 3 > 28?
- x > 4
- x > 5 ✓
- x > 6
- x > 7
解説
5x > 25 → x > 5.
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A line passes through (0, 6) and (3, 0). What is the slope of the line?
- −3
- −2 ✓
- 2
- 3
解説
Slope = (0 − 6)/(3 − 0) = −6/3 = −2.
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Given x + 2y = 10 and x = 4, what is y?
- 2
- 3 ✓
- 4
- 5
解説
Substitute x = 4: 4 + 2y = 10 → 2y = 6 → y = 3.
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Solve the system: 3x + y = 11 and x + y = 5. What is x?
- 2
- 3 ✓
- 4
- 5
解説
Subtract the second equation from the first: 2x = 6 → x = 3.
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A store charges $12 per hour to rent a kayak plus a $5 launch fee. How many hours can you rent if you have $53?
- 3
- 4 ✓
- 5
- 6
解説
12h + 5 = 53 → 12h = 48 → h = 4.
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The function f(x) = −4x + 20 represents the number of pages left in a book after x hours of reading. For what value of x does f(x) = 0?
- 4
- 5 ✓
- 6
- 8
解説
−4x + 20 = 0 → 4x = 20 → x = 5.
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If 2x + 3y = 18 and x = 3, what is y?
- 3
- 4 ✓
- 5
- 6
解説
2(3) + 3y = 18 → 6 + 3y = 18 → 3y = 12 → y = 4.
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For what value of k does the system kx + 2y = 8 and 3x + y = 6 have no solution?
- 3
- 6 ✓
- 1.5
- 2
解説
For no solution the lines must be parallel (equal slope ratios, unequal constant ratio). Multiply the second equation by 2: 6x + 2y = 12. For the x-coefficients to match, k = 6. Since 8 ≠ 12, the lines are parallel and the system has no solution.
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What is the solution set for |3x + 6| ≥ 9?
- x ≤ −5 or x ≥ 1 ✓
- x ≤ −5 or x ≥ −1
- x ≤ 1 or x ≥ 5
- −5 ≤ x ≤ 1
解説
3x + 6 ≥ 9 → x ≥ 1, or 3x + 6 ≤ −9 → 3x ≤ −15 → x ≤ −5. Solution: x ≤ −5 or x ≥ 1.
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A car rental company charges $25 per day plus $0.15 per mile. A competitor charges $40 per day with no mileage fee. For how many miles do both companies charge the same total for one day?
- 80
- 90
- 100 ✓
- 110
解説
25 + 0.15m = 40 → 0.15m = 15 → m = 100 miles.
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The equation 3x − 7 = ax + b has infinitely many solutions. What must be true?
- a = 3 and b = 7
- a = 3 and b = −7 ✓
- a = −3 and b = 7
- a = −3 and b = −7
解説
For infinitely many solutions the equation must be an identity: all coefficients and constants must match. So a = 3 (coefficient of x) and b = −7 (constant on the right equals −7 on the left).
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Line p has equation y = (2/3)x − 1. Line q is perpendicular to p and passes through (4, 3). What is the y-intercept of line q?
- 5
- 6
- 7
- 9 ✓
解説
Slope of p = 2/3, so slope of q = −3/2. Using point-slope: y − 3 = −(3/2)(x − 4) → y = −(3/2)x + 6 + 3 = −(3/2)x + 9. The y-intercept is 9.
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A number n satisfies 3n = 45. What is n?
- 12
- 13
- 14
- 15 ✓
解説
n = 45/3 = 15.
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A table shows (x, y) pairs: (0, 2), (1, 5), (2, 8), (3, 11). Which linear equation fits this data?
- y = 2x + 3
- y = 3x + 2 ✓
- y = x + 2
- y = 2x + 5
解説
Rate of change = (5−2)/(1−0) = 3; y-intercept = 2. Equation: y = 3x + 2.
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If −(3x − 4) = 10, what is x?
- −3
- −2 ✓
- −1
- 2
解説
−3x + 4 = 10 → −3x = 6 → x = −2.
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The system x − 3y = 1 and 2x + y = 9 is solved simultaneously. What is y?
- 0
- 1 ✓
- 2
- 3
解説
From the first equation: x = 1 + 3y. Substitute into the second: 2(1 + 3y) + y = 9 → 2 + 7y = 9 → 7y = 7 → y = 1.
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What is the x-coordinate of the intersection of y = −2x + 7 and y = 3x − 8?
- 1
- 2
- 3 ✓
- 4
解説
−2x + 7 = 3x − 8 → 15 = 5x → x = 3.
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In the linear equation 5x + 2y = k, the point (3, −1) lies on the line. What is k?
- 11
- 12
- 13 ✓
- 14
解説
5(3) + 2(−1) = 15 − 2 = 13.
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A student has at most $200 to spend on books. Each textbook costs $45 and each notebook costs $5. If she buys 3 textbooks, what is the maximum number of notebooks she can buy?
- 13 ✓
- 14
- 15
- 16
解説
45(3) + 5n ≤ 200 → 135 + 5n ≤ 200 → 5n ≤ 65 → n ≤ 13. Maximum is 13 notebooks.
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Which of the following is equivalent to 3(2x − 4) − 2(x + 1)?
- 4x − 10
- 4x − 14 ✓
- 8x − 14
- 4x + 14
解説
6x − 12 − 2x − 2 = 4x − 14.