Step 1: Subtract 4 from both sides: -2x > -4. Step 2: Divide by -2 (reverse the inequality): x < 2.

Step 1: Subtract 1 from both sides: -4x ≤ 8. Step 2: Divide by -4 (reverse inequality): x ≥ -2.

Step 1: Divide by 2: x - 3 > 2. Step 2: Add 3 to both sides: x > 5. Thus, x = 5 is a solution.

Step 1: Subtract 3 from both sides: 2x > 8. Step 2: Divide by 2: x > 4.

Step 1: Subtract 3 from both sides: 2x ≥ 8. Step 2: Divide by 2: x ≥ 4.

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

Step 1: Subtract 3x from both sides: x - 1 ≤ 2. Step 2: Add 1: x ≤ 3.

Step 1: Subtract 6 from both sides: -2x ≤ -2. Step 2: Divide by -2 (reverse the inequality): x ≥ 1.

Step 1: Subtract 7 from both sides: -2x > -6. Step 2: Divide by -2 (reverse the inequality): x < 3.

Step 1: Subtract 7 from both sides: -3x < -6. Step 2: Divide by -3 (reverse the inequality): x > 2.

Step 1: Subtract 7 from both sides: -x > -5. Step 2: Multiply by -1 (reverse the inequality): x < 5.

Step 1: Factor: (x + 4)(x - 2) < 0. Step 2: Critical points are x = -4 and x = 2. Step 3: Test intervals: valid for -4 < x < 2.

Step 1: Factor the inequality: x(x - 4) < 0. Step 2: The critical points are x = 0 and x = 4. Step 3: Test intervals: (0, 4) is valid.

Mean is a measure of central tendency, not dispersion.

The amplitude of a sine function y = Asin(Bx) is |A|. Here, A = 3, so the amplitude is 3.

cot(x) = 1/tan(x) = cos(x)/sin(x).

To factor, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).

First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).

Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor as (x + 2)(x + 3).

The polynomial factors to (x + 5)(x + 2) since 5 and 2 add to 7 and multiply to 10.

The polynomial can be factored as (x - 3)(x - 3) or (x - 3)^2.

Step 1: Recognize it as a difference of squares: a^2 - b^2 = (a - b)(a + b). Step 2: Here, a = x, b = 3. So, (x - 3)(x + 3).

cot(x) = cos(x)/sin(x) is the correct identity.

sin²(θ) + cos²(θ) = 1

The phase shift is found by setting the inside of the sine function to zero, giving a shift of π/4 to the right.

First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).

To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).

To factor x^2 - 5x + 6, find two numbers that multiply to 6 and add to -5.\nThe numbers are -2 and -3.\nThus, the factored form is (x - 2)(x - 3).

Mode is the number that appears most frequently. Here, 5 appears 3 times.

The Pythagorean identity is sin²θ + cos²θ = 1.