Explanation

The alternendo property states that if a/b = c/d, then:

a/c = b/d

Explanation

 Let's solve the equation:

(3/2)x - 5/2 = 1/2

Add 5/2 to both sides:

(3/2)x = 1/2 + 5/2

(3/2)x = 6/2

(3/2)x = 3

Multiply both sides by 2/3:

x = 3 × (2/3)

x = 2

Explanation

Let's denote the three consecutive natural numbers as x, x+1, and x+2. According to the problem:

x + (x + 1) + (x + 2) = 9

Combine like terms:

3x + 3 = 9

Subtract 3 from both sides:

3x = 6

Divide by 3:

x = 2

So, the numbers are:

x = 2

x + 1 = 3

x + 2 = 4

Explanation

The expression 16x² - 25y² is a difference of squares:

16x² - 25y² = (4x)² - (5y)²

Using the identity a² - b² = (a - b)(a + b), we get:

(4x)² - (5y)² = (4x - 5y)(4x + 5y)

So, the factors are:

(4x - 5y)(4x + 5y)

Explanation

Let's solve for t:

3t + 2 = 2t + 1

Subtract 2t from both sides:

t + 2 = 1

Subtract 2 from both sides:

t = -1