# Test: Linear Equations I - Challenging

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Question 1:   Solve: $2a-1=\sqrt{2}a+3$
$a=6\sqrt{2}$
$a=1+\sqrt{2}$
$a=4+2\sqrt{2}$
$a=\sqrt{2}$
Question 2:   Solve: $3\left(x-1\right)=-\sqrt{5}\left(x-\sqrt{5}\right)$
$x=-2\sqrt{5}$
$x=-3-\sqrt{5}$
$x=6-2\sqrt{5}$
$x=2+\sqrt{5}$
Question 3:   Solve the equation: $\left(x-4\right)\left(x+2\right)-{\left(x+1\right)}^{2}+x=0$
$x=-3$
$x=5$
$x=-4$
$x=2$
Question 4:   Solve the equation: ${\left(x+5\right)}^{2}={x}^{2}-5$
$x=-10$
$x=10$
$x=2$
$x=-3$
Question 5:   Solve the equation: $\frac{1}{2}x+\frac{3}{4}=\frac{2}{3}x-1$
$x=8$
$x=10.5$
$x=3.5$
$x=12$
Question 6:   Solve: $|3x|=1$
$x=\frac{1}{3}$
$x=-\frac{1}{3}$
$x=\frac{1}{3}$ or $x=-\frac{1}{3}$
Question 7:   Solve: $\frac{1+2a}{3}-\frac{2-a}{2}=-1$
$a=-\frac{2}{7}$
$a=0$
$a=1$
$a=-1$
Question 8:   Solve: $2m+3=5+\sqrt{2}m$
$m=2$
$m=\sqrt{2}$
$m=2+\sqrt{2}$
$x=-2+\sqrt{2}$
Question 9:   Solve: ${\left(2x-1\right)}^{2}-\left(2x+3\right)\left(2x-3\right)=0$
$x=1\frac{1}{2}$
$x=2\frac{1}{2}$
$x=-2$
$x=0$
Question 10:   Solve: $\sqrt{3-\frac{a+5}{2a+4}}=4$
$a=-1\frac{22}{25}$
$a=-2\frac{1}{9}$
$a=-2\frac{2}{27}$
$a=-1\frac{13}{25}$