Bluebook SAT Test Digital SAT Math Algebra Practice 1 — Questions and Answers
Question 1: If 3x + 7 = 22, what is the value of x?
- 3
- 5 (Correct answer)
- 7
- 9
Correct answer: 5
Subtract 7 from both sides: 3x = 15, then divide by 3: x = 5.
Starting with 3x + 7 = 22, subtract 7 from both sides to get 3x = 15. Divide both sides by 3 to find x = 5. Verify by substituting back: 3(5) + 7 = 15 + 7 = 22.
Question 2: A line passes through the points (2, 5) and (4, 11). What is the slope of the line?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
Slope = (y₂ − y₁)/(x₂ − x₁) = (11 − 5)/(4 − 2) = 6/2 = 3.
The slope formula is m = (y₂ − y₁)/(x₂ − x₁). Substituting the given points: m = (11 − 5)/(4 − 2) = 6/2 = 3. This means for every 1 unit increase in x, y increases by 3 units.
Question 3: Which of the following is the solution to the inequality 2x − 4 > 8?
- x > 2
- x > 6 (Correct answer)
- x < 6
- x < 2
Correct answer: x > 6
Add 4 to both sides: 2x > 12, then divide by 2: x > 6.
Starting with 2x − 4 > 8, add 4 to both sides: 2x > 12. Divide both sides by 2 (positive, so inequality direction stays the same): x > 6. Any value of x greater than 6 satisfies the inequality.
Question 4: If f(x) = 2x² − 3x + 1, what is f(3)?
- 8
- 10 (Correct answer)
- 12
- 14
Correct answer: 10
f(3) = 2(3)² − 3(3) + 1 = 2(9) − 9 + 1 = 18 − 9 + 1 = 10.
To evaluate f(3), replace every x with 3: f(3) = 2(3)² − 3(3) + 1 = 2(9) − 9 + 1 = 18 − 9 + 1 = 10. Always follow order of operations: exponents first, then multiplication, then addition/subtraction.
Question 5: The equation y = −2x + 6 represents a linear function. What is the y-intercept?
- −2
- 2
- 6 (Correct answer)
- −6
Correct answer: 6
In slope-intercept form y = mx + b, the y-intercept b = 6.
The equation y = −2x + 6 is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Here m = −2 (the slope) and b = 6 (the y-intercept). The line crosses the y-axis at (0, 6).
Question 6: If 4(x − 2) = 3x + 5, what is the value of x?
- 9
- 11
- 13 (Correct answer)
- 15
Correct answer: 13
Expand: 4x − 8 = 3x + 5. Subtract 3x: x − 8 = 5. Add 8: x = 13.
Distribute 4 on the left: 4x − 8 = 3x + 5. Subtract 3x from both sides: x − 8 = 5. Add 8 to both sides: x = 13. Check: 4(13 − 2) = 4(11) = 44 and 3(13) + 5 = 39 + 5 = 44.
Question 7: Which value of x satisfies both inequalities: x + 3 > 7 and 2x < 12?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
From x + 3 > 7: x > 4. From 2x < 12: x < 6. Only x = 5 satisfies 4 < x < 6.
Solve the first inequality: x + 3 > 7 → x > 4. Solve the second: 2x < 12 → x < 6. The solution is 4 < x < 6. Among the choices, only x = 5 falls in this range. Check: 5 + 3 = 8 > 7 and 2(5) = 10 < 12.
Bluebook SAT Test Digital SAT Math Algebra Practice 1
If 3x + 7 = 22, what is the value of x?