Linear equations and inequalities

1003046904

Level: 
B
We are given the inequality \( \frac1x+1 > \frac3{2x} \). Decide which of the following inequalities has the different solution set than the given inequality has, i.e. choose the inequality which is not equivalent to the given inequality.
\( 1+x > \frac32 \)
\( \frac2x+2>\frac3x \)
\( 1>\frac3{2x}-\frac1x \)
\( \frac1x-\frac3{2x}>-1 \)

1003046903

Level: 
B
We are given the inequality \( 3x+\frac{5-6x}2 > -2 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 0\cdot x > -9 \)
\( 0\cdot x > 9 \)
\( 0\cdot x < -9 \)
\( 3\cdot x > -9 \)

1003046902

Level: 
B
We are given the inequality \( 5-\frac{x+2}3 \leq \frac{2-x}6 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 26-2x \leq 2-x \)
\( 34-2x \leq 2-x \)
\( 26-2x \geq 2-x \)
\( 28-2x \leq 2-x \)

1003046901

Level: 
B
We are given the inequality \( -2x-\frac52 > 5-\frac x3 \). Decide which of the following inequalities is equivalent to the given inequality, i.e. which of the following inequalities was obtained from the given inequality by equivalent transformations.
\( 12x+15 < 2x-30 \)
\( 12x+15 > 2x-30 \)
\( 12x-15 > 2x-30 \)
\( 12x-15 < 2x+30 \)

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.
\( 1 \)