B | math4u.vsb.cz

1003044702

Level:

How many solutions does the following equation have? \[ 2^x\cdot3^{1-x}-2^{1-x}\cdot3^x=1 \]

Exactly one solution, \( x=0 \)

Exactly one solution, \( x=-1 \)

Exactly two solutions, \( x_1=-1\), \( x_2=0 \)

Exactly two solutions, \( x_1=-\frac23\), \( x_2=1 \)

1003044701

Level:

Identify the solution of the following equation. \[10\cdot25^x+10\cdot4^x=29\cdot10^x \]

\( x_1=-1,\ x_2=1 \)

The equation has no solution.

\( x_1=\frac25,\ x_2=\frac52 \)

\( x_1=-\frac52,\ x_2=-\frac25 \)

1003047107

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval. \[ |2x-1|+|2x|=|1-x|-|x+4| \]

\( (0.5,1) \)

\( (-4, 1) \)

\( (1,\infty) \)

\( (-4, 0) \)

1003047106

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are negative on this interval. \[ |5-x|-|x+3|=|x+1| \]

No such interval exists.

\( (-\infty,-3) \)

\( (-\infty,-1) \)

\( (-1, 5) \)

1003047105

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval. \[ |x+3|+|2x|=|x-1| \]

\( (1,\infty) \)

\( (-3,1) \)

\( (-3,\infty) \)

\( (-\infty,-3) \)

1003047104

Level:

Decide which of the following intervals ensures that the expressions in all the absolute values of the given equation are positive on this interval. \[ |2x+4|+|-x+1|=2x \]

\( (-2,1) \)

\( (-2,0) \)

\( ( 0,1) \)

\( (1,\infty) \)

1003047103

Level:

Find the set of the zero points of all the absolute values from the equation. \[ |-x+1|=|3x+9|-|2x|\] (The zero point is the value of \( x \) for which the absolute value equals zero.)

\( \{ -3,0,1 \} \)

\( \{ -3,-1,0 \} \)

\( \{ -3,0 \} \)

\( \{ -3,-1,3 \} \)

Find the sum of the zero points of all the absolute-value expressions of the equation. \[ |x-3|=|x+9|-|-2+x| \] (The zero point is the value of \( x \) for which the absolute-value expression equals zero.)

\( -4 \)

\( -8 \)

\( 14 \)

\( 10 \)

1003047101

Level:

Choose the equation which is, on the interval \( [-2, 3] \), equivalent to \[ |-x+3|+|x-7|=|x+2|. \]

\( (-x+3)-(x-7)=(x+2) \)

\( -(-x+3)+(x-7)=(x+2) \)

\( (-x+3)+(x-7)=-(x+2) \)

\( (-x+3)-(x-7)=-(x+2) \)

1003037502

Level:

Five more than one-third of the unknown number is smaller than three times the difference of this number and five. Which numbers do satisfy the given condition?

greater than \( \frac{15}2 \)

greater than \( \frac{15}4 \)

greater than \( \frac{25}4 \)

greater than \( \frac52 \)

B

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