Linear equations and inequalities

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.
\( -6+2x=x \)
\( -6-2x=x \)
\( -9+2x=x \)
\( -6-x=x \)

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.
\( 8x+12=2x \)
\( \frac{4x}{x+2}+\frac6{x+2}=\frac x{x+2} \)
\( \frac{6x}{x+2}=-\frac{12}{x+2} \)
\( \frac x{x+2}=-\frac2{x+2} \)

1103049404

Level: 
A
In addition to solving equation \( ax+b=cx+d \) algebraically, you can also solve it graphically. When the lines \( y=ax+b \) and \( y=cx+d \) are graphed, you look for the intersection of these lines. In the pictures below are graphed lines \( y=ax+b \) and \( y=cx+d\). Choose the picture in which the equation \( ax+b=cx+d \) has only one non-negative solution.