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:
[tex]\frac{x}{2} = \frac{y - 5}{5}[/tex]
Solution:
Given that,
[tex]\frac{x + 2}{2} = \frac{y}{5}[/tex]
The above expression can be rewritten as:
[tex]\frac{x}{2} + \frac{2}{2} = \frac{y}{5}\\\\Simplify\\\\\frac{x}{2} + 1 = \frac{y}{5}[/tex]
Move the constant 1 from left side of equation to right side of equation
[tex]\frac{x}{2} = \frac{y}{5} - 1[/tex]
Simplify the right side of equation by making the denominator same
[tex]\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}[/tex]
Thus [tex]\frac{x}{2} = \frac{y - 5}{5}[/tex] is true
