Linear equations and inequalities

1003047003

Level: 
A
We are given the equation \( \frac{8x}{x+2}+\frac{12}{x+2}=\frac{2x}{x+2} \). Decide which of the following equations has the different set of roots than the given equation has, i.e. choose the equation which is not equivalent to the given equation.
\( 8x+12=2x \)
\( \frac{4x}{x+2}+\frac6{x+2}=\frac x{x+2} \)
\( \frac{6x}{x+2}=-\frac{12}{x+2} \)
\( \frac x{x+2}=-\frac2{x+2} \)

1003047002

Level: 
A
We are given the equation \( 1-\frac{5-x}2=\frac x4 \). Decide which of the following equations is equivalent to the given equation, i.e. which of the following equations was obtained from the given equation by equivalent transformations.
\( -6+2x=x \)
\( -6-2x=x \)
\( -9+2x=x \)
\( -6-x=x \)

1003037305

Level: 
A
Suppose we increase the numerator of five-ninth by an integer and we decrease the denominator of five-ninth by the same integer. We get the fraction with numerator six times greater than the denominator. Find the integer.
\( 7 \)
\( 3 \)
There is no such an integer.
\( 1 \)