# Test: Linear equations II - Challenging

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Question 1:   Solve  $\frac{1}{2}x-1=\frac{1}{3}x$
$-6$
$\frac{1}{6}$
$6$
$-\frac{1}{6}$
Question 2:   Solve  $\frac{x-3}{3}-\frac{2x}{9}=2$
$-27$
$27$
$0$
$1$
Question 3:   Solve  $1+\frac{x+17}{5}=\frac{3x-7}{4}$
$-11\frac{2}{11}$
$11\frac{2}{11}$
$\frac{11}{123}$
$-\frac{11}{123}$
Question 4:   From two sites collected  $46kg$  of tomato. How many vegetables were collected from each plot if the second harvested  $6kg$  more than the first?
$16kg$  and  $26kg$
$10kg$  and  $36kg$
$16kg$  and  $30kg$
$20kg$  and  $26kg$
Question 5:   Father is  $35$  years old and the son is  $12$  years old. In how many years father will be twice as old as the son?
$12$  years
$10$  years
$2$  years
$11$  years
Question 6:   The boat traveled the distance between the two marinas for  $2$  hours and back for  $3$  hours. The current speed is  $2km}{h}$ .  Find the speed of the boat.
$10km}{h}$
$15km}{h}$
$12km}{h}$
$11km}{h}$
Question 7:   Solve  $\left|2x\right|=8$
$0$
$4$
$-4$
$4$  and  $-4$
Question 8:   Solve  $\left|5-3x\right|=9$
$1\frac{1}{3}$  and  $4\frac{2}{3}$
$1\frac{1}{3}$
$4\frac{2}{3}$
$-1\frac{1}{3}$  and  $4\frac{2}{3}$
Question 9:   Solve the equation  $\left|\left|x\right|-4\right|=1$
$\begin{array}{l}x=-5\\ x=-3\end{array}$

$\begin{array}{l}x=5\\ x=-3\end{array}$

$\begin{array}{l}x=5\\ x=3\end{array}$

$\begin{array}{l}x=5\\ x=-5\\ x=3\\ x=-3\end{array}$

Question 10:   For which values of  $a$  expression  $ax=4+a$  have no roots?
$0$
$-4$
$4$
$1$