Explanation

Let's solve the equation:

2(x - 2) - 5(x - 5) = 4(x - 8) - 2(x - 2)

Expanding both sides:

2x - 4 - 5x + 25 = 4x - 32 - 2x + 4

Combine like terms:

-3x + 21 = 2x - 28

Add 3x to both sides:

21 = 5x - 28

Add 28 to both sides:

49 = 5x

Divide by 5:

x = 49/5

Explanation

To evaluate the expression 1/2 + 1/3 - 1/4, we need to find a common denominator. The least common multiple of 2, 3, and 4 is 12.

1/2 = 6/12

1/3 = 4/12

1/4 = 3/12

Now, let's add and subtract:

6/12 + 4/12 - 3/12

= (6 + 4 - 3)/12

= 7/12

Explanation

To find the greatest number of kits they can make, we need to determine the greatest common divisor (GCD) of the quantities of each type of bandage: 30, 60, and 75.

The prime factorization of each number is:

30 = 2 × 3 × 5

60 = 2² × 3 × 5

75 = 3 × 5²

The common factors are 3 and 5, so the GCD is 3 × 5 = 15.

Thus, they can make 15 kits.

Explanation

A composite number is a positive integer that has at least one positive divisor other than 1 and itself.

Let's examine the numbers:

4: divisors are 1, 2, and 4 (composite)

9: divisors are 1, 3, and 9 (composite)

15: divisors are 1, 3, 5, and 15 (composite)

Since all numbers (4, 9, 15) have divisors other than 1 and themselves, they are composite numbers.

The group 4, 9, 15 consists entirely of composite numbers.

Explanation

A number divisible by both 2 and 5 is automatically divisible by their LCM = 10.

For example, 20 ÷ 2 = 10, 20 ÷ 5 = 4, and 20 ÷ 10 = 2.