Bluebook SAT Algebra Practice — Questions and Answers
Question 1: If 3(x - 4) + 2x = 5x - 7 + k, for what value of k does the equation have infinitely many solutions?
- -5 (Correct answer)
- -12
- 5
- 12
Correct answer: -5
Expanding gives 5x - 12 = 5x - 7 + k, so k = -5.
Expand the left side: 3x - 12 + 2x = 5x - 12. The equation becomes 5x - 12 = 5x - 7 + k. For infinitely many solutions, both sides must be identical, so -12 = -7 + k, giving k = -5.
Question 2: The line y = mx + b passes through the points (2, 7) and (5, 16). What is the value of b?
- 3
- 1 (Correct answer)
- -1
- 9
Correct answer: 1
The slope is 3, and substituting (2, 7) gives 7 = 6 + b, so b = 1.
Slope m = (16 - 7)/(5 - 2) = 9/3 = 3. Substitute (2, 7) into y = 3x + b: 7 = 3(2) + b, so 7 = 6 + b and b = 1. Check with (5, 16): 3(5) + 1 = 16.
Question 3: A phone plan charges a flat monthly fee plus a fixed rate per gigabyte of data. A customer who uses 4 gigabytes pays $34, and a customer who uses 9 gigabytes pays $54. What is the flat monthly fee, in dollars?
- 4
- 20
- 14
- 18 (Correct answer)
Correct answer: 18
Rate is $4/GB, so fee = 34 - 4(4) = 18.
Let the fee be f and the rate be r. Then f + 4r = 34 and f + 9r = 54. Subtracting, 5r = 20, so r = 4. Substituting, f + 16 = 34, so f = 18.
Question 4: Which of the following systems of equations has no solution?
- y = 2x + 1 and y = -2x + 1
- 2x + 4y = 8 and x + 2y = 4
- 3x - y = 5 and 6x - 2y = 9 (Correct answer)
- x + y = 3 and x - y = 1
Correct answer: 3x - y = 5 and 6x - 2y = 9
Both lines have slope 3 but different intercepts, so they are parallel.
A system has no solution when the lines are parallel but distinct. In choice C, 6x - 2y = 9 simplifies to 3x - y = 4.5, which has the same slope as 3x - y = 5 but a different constant, so the lines never meet. Choice B is the same line twice (infinitely many solutions), and choices A and D each intersect at one point.
Question 5: If 2/(x + 1) = 5/(3x - 2), what is the value of x?
- 9 (Correct answer)
- -9
- 1
- -1
Correct answer: 9
Cross-multiplying gives 6x - 4 = 5x + 5, so x = 9.
Cross-multiply: 2(3x - 2) = 5(x + 1). This gives 6x - 4 = 5x + 5. Subtract 5x from both sides: x - 4 = 5, so x = 9. Neither denominator is zero at x = 9, so the solution is valid.
Question 6: The inequality 4 - 3x > 2x - 11 is equivalent to which of the following?
- x > 3
- x < 3 (Correct answer)
- x > -3
- x < -3
Correct answer: x < 3
Collecting terms gives 15 > 5x, so x < 3.
Add 3x to both sides: 4 > 5x - 11. Add 11: 15 > 5x. Divide by 5 (positive, so no flip): 3 > x, which is x < 3. Check: x = 0 gives 4 > -11, true; x = 4 gives -8 > -3, false.
Bluebook SAT Algebra Practice
If 3(x - 4) + 2x = 5x - 7 + k, for what value of k does the equation have infinitely many solutions?