3D Geometry

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Q1. What is the value of x in the inequality 3x - 7 < 2?

Solution:

Step 1: Add 7 to both sides: 3x < 9. Step 2: Divide by 3: x < 3.

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Q2. What is the solution to the equation 5x + 2 = 17?

Solution:

Step 1: Subtract 2 from both sides: 5x = 15. Step 2: Divide by 5: x = 3.

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Q3. What is the value of x in the polynomial equation 3x^2 + 12x = 0?

Solution:

Step 1: Factor out 3x: 3x(x + 4) = 0. Step 2: Set each factor to zero: 3x = 0 or x + 4 = 0. Step 3: Solutions are x = 0 and x = -4.

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Q4. Which of the following is a solution to the equation 3x + 7 = 16?

Solution:

Step 1: Subtract 7 from both sides: 3x = 9. Step 2: Divide both sides by 3: x = 3.

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Q5. What is the result of factoring the polynomial x^2 + 7x + 10?

Solution:

Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor: (x + 5)(x + 2).

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Q6. What is the factored form of the quadratic x^2 - 5x + 6?

Solution:

Find two numbers that multiply to 6 and add to -5: -2 and -3. Thus, (x - 2)(x - 3).

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Q7. What is the factored form of the polynomial x^2 - 9?

Solution:

Step 1: Recognize it as a difference of squares: x^2 - 3^2. Step 2: Factor: (x - 3)(x + 3).

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Q8. Which of the following is a factor of the polynomial x^2 - 5x + 6?

Solution:

Step 1: Factor the polynomial: (x - 2)(x - 3). Step 2: The factors are (x - 2) and (x - 3).

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Q9. What is the solution to the equation 7x + 2 = 3x + 18?

Solution:

Step 1: Subtract 3x from both sides: 4x + 2 = 18. Step 2: Subtract 2: 4x = 16. Step 3: Divide by 4: x = 4.

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Q10. Solve the inequality 5x - 2 < 3.

Solution:

Step 1: Add 2 to both sides: 5x < 5. Step 2: Divide both sides by 5: x < 1.