Equations — Quiz 6

Questions in this quiz (6)

1. Solve the equation:$$\frac{x-1}{x+1}+\frac{x+1}{x-1}=\frac{x-2}{x+2}+\frac{x+2}{x-2}$$

   • 1
   • 0
   • -1
   • No solution

2. The supervisor in charge of the activities office rented buses from one of the transportation companies in order to organize a tourist trip. If we distribute the students onto the buses at a rate of 38 students per bus, then 13 students will remain without a seat. But if we distribute the students onto the buses at a rate of 42 students per bus, then 15 seats will remain empty. How many students are there in total, and how many buses were rented?

   • 279 students, 7 buses
   • 80 students, 13 buses
   • 75 students, 15 buses
   • 79 students, 13 buses

3. Solve the equation: $$\left|x - \left|x + 4\right|\right| = 6$$

   • -5
   • 1
   • $$-5, 1$$
   • -4

4. Solve the equation: $$|x - |x + |x + 2|| | = 4$$

   • $${-2, 2}$$
   • $${-6, -2}$$
   • $${-2, 6}$$
   • $${-6, 2}$$

5. Solve the equation: $$2^{2x} \cdot 5^{3x} = 10^{4x}$$

   • $$\frac{1}{2}$$
   • $$\frac{1}{4}$$
   • $$\frac{1}{3}$$
   • 0

6. Solve the equation: $$x^{\log_2 x} = 16$$

   • $${-2, \frac{1}{4}}$$
   • $$\frac{1}{4}$$
   • $$4$$
   • $$-2$$