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
3821
If 8 - x = 2x - 7, then x is:
Answer:
5
Add x to both sides: 8 = 3x - 7. Add 7: 15 = 3x. Divide by 3: x = 5.
3822
Solve for y: (y + 5)/3 - y/2 = 1
Answer:
4
Multiply by LCM 6: 2(y + 5) - 3y = 6. Expand: 2y + 10 - 3y = 6. Combine: -y + 10 = 6. Subtract 10: -y = -4. y = 4.
3823
Seven times a number is 35. The number is:
Answer:
5
The equation is 7n = 35. Divide by 7: n = 5.
3824
Solve the equation: 3(x + 2) = 2(x - 1) + 15
Answer:
7
Expand: 3x + 6 = 2x - 2 + 15. Combine: 3x + 6 = 2x + 13. Subtract 2x: x + 6 = 13. Subtract 6: x = 7.
3825
If x/4 = 2x/5 - 3, find x.
Answer:
20
Subtract x/4 from both sides and add 3 to both sides: 3 = 2x/5 - x/4. Common denominator (20): 3 = (8x - 5x) / 20. This gives 3 = 3x / 20. Multiply by 20/3: x = 20.
3826
Solve for k: 4k - 2(k + 3) = 10
Answer:
8
Expand: 4k - 2k - 6 = 10. Combine: 2k - 6 = 10. Add 6: 2k = 16. Divide by 2: k = 8.
3827
The sum of two numbers is 35 and their difference is 13. Find the smaller number.
Answer:
11
Let numbers be x and y. x + y = 35 and x - y = 13. Adding them: 2x = 48, so x = 24. Substituting into the first equation: 24 + y = 35, so y = 11. The smaller number is 11.
3828
Solve the equation: (x - 3)/2 = (2x + 1)/5
Answer:
17
Cross-multiply: 5(x - 3) = 2(2x + 1). Expand: 5x - 15 = 4x + 2. Subtract 4x: x - 15 = 2. Add 15: x = 17.
3829
If 5x - 3 = 12, what is the value of x^2 + 1?
Answer:
10
First, solve for x. Add 3: 5x = 15. Divide by 5: x = 3. Now find x^2 + 1: 3^2 + 1 = 9 + 1 = 10.
3830
Solve for a: 2(a - 1) + 3(a + 2) = 24
Answer:
4
Expand: 2a - 2 + 3a + 6 = 24. Combine: 5a + 4 = 24. Subtract 4: 5a = 20. Divide by 5: a = 4.