BMST - Basic Math and Science Algebraic Equations and Inequalities Questions and Answers 2 — Questions and Answers

Question 1: Solve for x: 3(x - 4) = 2x + 5

x = 17 (Correct answer)
x = 7
x = -7
x = 1

Correct answer: x = 17

Distribute 3 to get 3x - 12 = 2x + 5. Subtract 2x from both sides: x - 12 = 5. Add 12: x = 17.

To solve 3(x - 4) = 2x + 5, first apply the distributive property: 3x - 12 = 2x + 5. Next, isolate the variable by subtracting 2x from both sides to get x - 12 = 5. Finally, add 12 to both sides to find x = 17. You can verify by substituting back: 3(17 - 4) = 3(13) = 39, and 2(17) + 5 = 34 + 5 = 39.

Question 2: Which inequality represents 'a number decreased by 8 is at most 15'?

x - 8 ≤ 15 (Correct answer)
x - 8 ≥ 15
x - 8 < 15
8 - x ≤ 15

Correct answer: x - 8 ≤ 15

'Decreased by 8' means subtract 8, and 'at most' means less than or equal to.

The phrase 'a number decreased by 8' translates to x - 8. The phrase 'at most 15' means the result can equal 15 or be less than 15, which uses the ≤ symbol. Therefore the correct inequality is x - 8 ≤ 15. Solving gives x ≤ 23.

Question 3: What is the solution to the system: x + y = 10 and x - y = 4?

x = 7, y = 3 (Correct answer)
x = 3, y = 7
x = 8, y = 2
x = 6, y = 4

Correct answer: x = 7, y = 3

Adding both equations eliminates y: 2x = 14, so x = 7. Then y = 10 - 7 = 3.

When you add the equations x + y = 10 and x - y = 4, the y terms cancel: (x + y) + (x - y) = 10 + 4, giving 2x = 14, so x = 7. Substituting back into x + y = 10 gives 7 + y = 10, so y = 3. Verify with the second equation: 7 - 3 = 4.

Question 4: Simplify: 5x² + 3x - 2x² + 7x

3x² + 10x (Correct answer)
7x² + 10x
3x² + 4x
7x² + 4x

Correct answer: 3x² + 10x

Combine like terms: 5x² - 2x² = 3x² and 3x + 7x = 10x.

To simplify this expression, identify and combine like terms. The x² terms are 5x² and -2x², which combine to 3x². The x terms are 3x and 7x, which combine to 10x. The simplified expression is 3x² + 10x.

Question 5: If 2x + 9 > 25, what is the solution set?

x > 8 (Correct answer)
x > 17
x < 8
x ≥ 8

Correct answer: x > 8

Subtract 9 from both sides: 2x > 16. Divide by 2: x > 8.

Start with 2x + 9 > 25. Subtract 9 from both sides to get 2x > 16. Then divide both sides by 2 (since 2 is positive, the inequality direction stays the same) to get x > 8. Any value greater than 8 satisfies this inequality.

Question 6: Factor the expression: x² - 9

(x + 3)(x - 3) (Correct answer)
(x - 3)(x - 3)
(x + 9)(x - 1)
(x + 3)(x + 3)

Correct answer: (x + 3)(x - 3)

This is a difference of squares: a² - b² = (a + b)(a - b), where a = x and b = 3.

The expression x² - 9 is a difference of squares because x² = (x)² and 9 = (3)². The difference of squares formula states that a² - b² = (a + b)(a - b). Applying this with a = x and b = 3 gives (x + 3)(x - 3). You can verify by expanding: x² - 3x + 3x - 9 = x² - 9.

BMST - Basic Math and Science Algebraic Equations and Inequalities Questions and Answers 2

Solve for x: 3(x - 4) = 2x + 5