Indices and Surds

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Q1. Which of the following is the solution to the inequality 2x + 1 > 3?

Solution:

Step 1: Subtract 1 from both sides: 2x > 2. Step 2: Divide by 2: x > 1.

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Q2. What is the solution to the equation 7x - 2 = 5x + 6?

Solution:

Step 1: Subtract 5x from both sides: 2x - 2 = 6. Step 2: Add 2 to both sides: 2x = 8. Step 3: Divide by 2: x = 4.

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Q3. What is the simplified form of the expression 2√(8) + 3√(2)?

Solution:

Step 1: Simplify 2√(8) = 2 * 2√(2) = 4√(2). Step 2: Combine: 4√(2) + 3√(2) = 7√(2).

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Q4. What is the simplified form of the expression 2(x + 3) - 4?

Solution:

Step 1: Distribute: 2x + 6 - 4. Step 2: Combine like terms: 2x + 2.

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Q5. Which of the following is the solution to the equation 4x^2 - 12x + 9 = 0?

Solution:

Step 1: Factor the equation: (2x - 3)(2x - 3) = 0. Step 2: Set the factor to zero: 2x - 3 = 0. Step 3: Solve for x: x = 3/2.

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Q6. Which of the following represents the expression 2x^2 + 8x factored?

Solution:

Step 1: Factor out the common term 2x: 2x(x + 4).

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Q7. Which of the following is the solution to the inequality 2x + 3 ≥ 7?

Solution:

Step 1: Subtract 3 from both sides: 2x ≥ 4. Step 2: Divide both sides by 2: x ≥ 2.

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Q8. What is the simplified form of the expression 2√18 + 3√8?

Solution:

Step 1: Simplify √18 = 3√2 and √8 = 2√2. Step 2: Substitute: 2(3√2) + 3(2√2) = 6√2 + 6√2 = 12√2.