Question

If (x+2/2 = y/5, then which of the following must be true?

Answer 1

Question:

If (x + 2)/2 = y /5, then which of the following must be true?

x/2 = (y-2)/5

x/2 = (y-5)/5

(x+2)/5 = y/25

Answer:

The true is:

$\frac{x}{2} = \frac{y - 5}{5}$

Solution:

Given that,

$\frac{x + 2}{2} = \frac{y}{5}$

The above expression can be rewritten as:

$\frac{x}{2} + \frac{2}{2} = \frac{y}{5}\\\\Simplify\\\\\frac{x}{2} + 1 = \frac{y}{5}$

Move the constant 1 from left side of equation to right side of equation

$\frac{x}{2} = \frac{y}{5} - 1$

Simplify the right side of equation by making the denominator same

$\frac{x}{2} = \frac{y}{5} - \frac{ 1 \times 5}{ 1 \times 5}\\\\\frac{x}{2} = \frac{y}{5} - \frac{ 5}{ 5}\\\\\frac{x}{2} = \frac{y - 5}{5}$

Thus $\frac{x}{2} = \frac{y - 5}{5}$ is true