Let the number of girls be x. Then the number of boys is 2x. The equation is x + 2x = 120. Solving gives 3x = 120, so x = 40. Therefore, boys = 2x = 80.

Let the number of boys be 3x and the number of girls be 2x. Then, 3x + 2x = 300. This gives 5x = 300, so x = 60. Therefore, the number of girls is 2x = 120.

Let the number of girls be 3x and boys be 5x. The equation is 3x + 5x = 64. Solving gives 8x = 64, so x = 8. Therefore, girls = 3x = 24.

Let the speed of the train on the way to the destination be x km/h. The time taken to travel to the destination is 60/x hours and the time taken to return is 60/90 hours. The total time is given by: 60/x + 60/90 = 4. Solving for x gives x = 40 km/h.

Distance = Speed × Time. Therefore, Distance = 60 km/h × t h = 60t km.

Step 1: Expand: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

Step 1: Factor the inequality: 2(x^2 - 4) < 0. Step 2: Roots are x = -2 and x = 2. Step 3: The solution is between the roots: (-2, 2).

Step 1: Factor the quadratic: (x + 3)(x + 1) < 0. Step 2: The critical points are x = -3 and x = -1. Step 3: Test intervals: The solution set is (-3, -1).

Step 1: Factor: (x - 2)(x - 4) ≤ 0. Step 2: The solution is between the roots: [2, 4].

Set y = 0: x^2 - 4 = 0. Factoring gives (x - 2)(x + 2) = 0. Thus, x = 2 and x = -2.

First, factor out the common term 2: 2(x^2 + 4x + 3). Then, factor the quadratic: 2(x + 3)(x + 1).

To factor 2x^2 - 8, first factor out 2: 2(x^2 - 4). Then, recognize x^2 - 4 as a difference of squares: 2(x - 2)(x + 2).

First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 3(x - 2)(x + 2).

The expression 4x^2 - 12x + 9 is also a perfect square trinomial. It factors to (2x - 3)(2x - 3) or (2x - 3)^2.

First, factor out the greatest common factor, which is 4. This gives us 4(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 4(x - 2)(x + 2).

We need two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the factored form is (x + 6)(x - 2).

The expression x^2 - 4 is a difference of squares. It factors to (x - 2)(x + 2).

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

The expression 4x^2 - 25 is a difference of squares. It can be factored as (2x - 5)(2x + 5).

We need two numbers that multiply to -10 and add to 3. The numbers 5 and -2 work. Thus, the factorization is (x + 5)(x - 2).

The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.

To factor x^2 + 7x + 10, we need two numbers that multiply to 10 and add to 7. The numbers 2 and 5 work. Thus, the factorization is (x + 2)(x + 5).

To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).

The expression x^2 - 9 is a difference of squares. It can be factored as (x - 3)(x + 3).

Factor out the common term 2: 2(x^2 - 4) = 2(x - 2)(x + 2).

First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, factor x^2 - 4 as a difference of squares: 3(x - 2)(x + 2).

To factor, we look for two numbers that multiply to 10 and add to 7. The numbers are 5 and 2. Thus, the factorization is (x + 5)(x + 2).

To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).

The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).

First, factor out the common term x: x(x^2 - 3x - 4). Now, factor the quadratic x^2 - 3x - 4 to get x(x - 4)(x + 1).