Practice Test

Graph the following: $2 y = 3 x + 4.$

Find the x- and y-intercepts for the following: $2 x - 5 y = 6$

Find the x- and y-intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.

$3 x - 4 y = 12$

Find the exact distance between $(5, −3)$ and $(- 2, 8) .$ Find the coordinates of the midpoint of the line segment joining the two points.

Write the interval notation for the set of numbers represented by ${x | x \leq 9} .$

Solve for x: $5 x + 8 = 3 x - 10.$

Solve for $x$ : $3 (2 x - 5) - 3 (x - 7) = 2 x - 9.$

Solve for x: $\frac{x}{2} + 1 = \frac{4}{x}$

Solve for x: $\frac{5}{x + 4} = 4 + \frac{3}{x - 2} .$

10.

The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

11.

Solve for x. Write the answer in simplest radical form.

$\frac{x^{2}}{3} - x = - \frac{1}{2}$

12.

Solve: $3 x - 8 \leq 4.$

13.

Solve: $| 2 x + 3 | < 5.$

14.

Solve: $| 3 x - 2 | \geq 4.$

For the following exercises, find the equation of the line with the given information.

15.

Passes through the points $(- 4, 2)$ and $(5, −3) .$

16.

Has an undefined slope and passes through the point $(4, 3) .$

17.

Passes through the point $(2, 1)$ and is perpendicular to $y = - \frac{2}{5} x + 3.$

18.

Add these complex numbers: $(3 - 2 i) + (4 - i) .$

19.

Simplify: $\sqrt{−4} + 3 \sqrt{−16} .$

20.

Multiply: $5 i (5 - 3 i) .$

21.

Divide: $\frac{4 - i}{2 + 3 i} .$

22.

Solve this quadratic equation and write the two complex roots in $a + b i$ form: $x^{2} - 4 x + 7 = 0.$

23.

Solve: ${(3 x - 1)}^{2} - 1 = 24.$

24.

Solve: $x^{2} - 6 x = 13.$

25.

Solve: $4 x^{2} - 4 x - 1 = 0$

26.

Solve: $\sqrt{x - 7} = x - 7$

27.

Solve: $2 + \sqrt{12 - 2 x} = x$

28.

Solve: ${(x - 1)}^{\frac{2}{3}} = 9$

For the following exercises, find the real solutions of each equation by factoring.

29.

$2 x^{3} - x^{2} - 8 x + 4 = 0$

30.

${(x + 5)}^{2} - 3 (x + 5) - 4 = 0$