All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3861
Solve the equation: 3(2x - 5) - 4(x - 3) = 5
Answer:
4
Expand all terms: 6x - 15 - 4x + 12 = 5. Combine like terms: 2x - 3 = 5. Add 3: 2x = 8. Divide by 2: x = 4.
3862
If x - 20% of x = 40, find x.
Answer:
50
The equation is x - 0.20x = 40, which simplifies to 0.80x = 40. Divide by 0.80: x = 40 / 0.80 = 50.
3863
Solve for y: (2y + 1)/5 = (y - 1)/2
Answer:
7
Cross-multiply: 2(2y + 1) = 5(y - 1). Expand: 4y + 2 = 5y - 5. Subtract 4y from both sides: 2 = y - 5. Add 5: y = 7.
3864
A number is doubled and then 9 is added. If the result is 35, what is the number?
Answer:
13
Let the number be x. The equation is 2x + 9 = 35. Subtract 9: 2x = 26. Divide by 2: x = 13.
3865
Solve the equation: 3x/4 - 2 = x/4 + 6
Answer:
16
Subtract x/4 from both sides: 3x/4 - x/4 - 2 = 6, which simplifies to 2x/4 - 2 = 6, or x/2 - 2 = 6. Add 2: x/2 = 8. Multiply by 2: x = 16.
3866
If 10x - 5 = 25, find the value of x/2.
Answer:
1.5
First, solve for x. Add 5: 10x = 30. Divide by 10: x = 3. The question asks for x/2, so 3 / 2 = 1.5.
3867
Solve for z: z - (z - 1)/2 = 3
Answer:
5
Multiply the entire equation by 2 to clear the fraction: 2z - (z - 1) = 6. Distribute the negative sign: 2z - z + 1 = 6. Combine terms: z + 1 = 6. Subtract 1: z = 5.
3868
Two times a number is 15 less than three times the same number. Find the number.
Answer:
15
Let the number be n. The equation is 2n = 3n - 15. Subtract 3n from both sides: -n = -15. Multiply by -1: n = 15.
3869
Solve the equation: 5(x - 2) + 3(x + 1) = 25
Answer:
4
Expand all terms: 5x - 10 + 3x + 3 = 25. Combine like terms: 8x - 7 = 25. Add 7: 8x = 32. Divide by 8: x = 4.
3870
If 3a + 5 = a - 3, then a is:
Answer:
-4
Subtract 'a' from both sides: 2a + 5 = -3. Subtract 5 from both sides: 2a = -8. Divide by 2: a = -4.