Q1. Which of the following is a solution to the inequality 2x + 3 > 7?
Solution:
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2. The solution includes all values greater than 2.
⏱ Time: 0s
Q2. What is the result of (2x + 3)(x - 1)?
Solution:
Step 1: Use the distributive property: 2x^2 - 2x + 3x - 3. Step 2: Combine like terms: 2x^2 + x - 3.
⏱ Time: 0s
Q3. Solve for x: 4(x - 1) = 2(x + 3).
Solution:
Step 1: Distribute: 4x - 4 = 2x + 6. Step 2: Subtract 2x from both sides: 2x - 4 = 6. Step 3: Add 4 to both sides: 2x = 10. Step 4: Divide by 2: x = 5.
⏱ Time: 0s
Q4. If 2x + 5 = 3x - 1, what is the value of x?
Solution:
Rearranging gives: 5 + 1 = 3x - 2x, thus x = 6.
⏱ Time: 0s
Q5. What is the vertex of the parabola given by the equation y = x^2 - 4x + 3?
Solution:
Step 1: Use the vertex formula x = -b/(2a): x = 4/(2*1) = 2. Step 2: Substitute x back into the equation: y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1. Step 3: Vertex is (2, -1).
⏱ Time: 0s
Q6. What is the result of (x + 2)(x - 3)?
Solution:
Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.
⏱ Time: 0s
Q7. Solve for x: x^2 - 5x + 6 = 0.
Solution:
Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.
⏱ Time: 0s
Q8. Which expression represents the difference of squares for a^2 - b^2?
Solution:
The difference of squares is factored as (a + b)(a - b).
⏱ Time: 0s
Q9. What is the product of (x + 1)(x + 4)?
Solution:
Step 1: Use the distributive property: x^2 + 4x + x + 4. Step 2: Combine like terms: x^2 + 5x + 4.
⏱ Time: 0s
Q10. What is the value of x in the equation 4x^2 - 12x + 9 = 0?
Solution:
Factor the equation: (2x - 3)(2x - 3) = 0. Thus, x = 3.
