2000002305
Level:
A
Find a real number, so that when placed into the box, the given equation has the root \(x = 3\).
\[\frac{2}{3}x-5= \fbox{$\phantom{5}$}\cdot x-1 \]
\( -\frac{2}{3} \)
\( 6 \)
\( 2 \)
\( \frac{4}{3} \)
Linear equations and inequalities
2010009001
Level:
A
Find the solution set of the following equation.
\[\frac{x+5}3-\frac x2=\frac{2x-2}3-\frac{x-3}2 \]
\( \left\{\frac52 \right\} \)
\( \left\{\frac{23}2\right\} \)
\( \mathbb{R} \)
\( \emptyset \)
2010009002
Level:
A
Find the solution set of the following equation.
\[\frac{3+2x}2-\frac76=5x-\frac{12x-1}3 \]
\( \mathbb{R} \)
\( \{1\} \)
\( \{0\} \)
\( \emptyset \)
2010009003
Level:
A
Find the solution set of the following equation.
\[3x-2[x-3(x+1)]=7x+6 \]
\( \mathbb{R} \)
\( \{-1\} \)
\( \{0\} \)
\( \emptyset \)
2010009004
Level:
A
Find the solution set of the following equation.
\[x-3[x-5(x-4)]=10(x-3) \]
\( \{10\} \)
\( \left\{-\frac{10}9\right\} \)
\( \{-14\} \)
\( \emptyset \)
2010009005
Level:
A
Find the solution set of the following equation.
\[(x+3)^2-(2-2x)^2=1-3x^2 \]
\( \left\{-\frac27\right\} \)
\( \{2\} \)
\( \left\{\frac72\right\} \)
\( \emptyset \)
2010009006
Level:
A
Find the solution set of the following equation.
\[(x-2)^2+(2+x)^2=8+2x^2 \]
\( \mathbb{R}\)
\( \{-1\} \)
\( \{2\} \)
\( \{-2\} \)
2010015401
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac12x+2=5-x\)
\( x+2=-x+5 \)
\( \frac14x+2=5-x \)
\( -x+2=5-\frac12x \)
2010015402
Level:
A
Choose the equation whose graphical solution is in the picture.
\( \frac25x-2=-4x+4\)
\( \frac52x-2=-4x+4\)
\( \frac12x-2=-x+4\)
\( \frac25x-2=-x+4\)
2010015403
Level:
A
Choose the equation whose graphical solution is in the picture.
\( -\frac49x+1=\frac29x-2\)
\( -\frac94x+1=\frac29x-2\)
\( -\frac49x+1=\frac92x-2\)
\( -\frac94x+1=\frac92x-2\)