### Practice Test

Find the *x-* and *y*-intercepts for the following: $2x\xe2\u02c6\u20195y=6$

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

$3x\xe2\u02c6\u20194y=12$

Find the exact distance between $\left(5,\mathrm{\xe2\u02c6\u20193}\right)$ and $\left(\xe2\u02c6\u20192,8\right).$ 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 $\left\{x|x\xe2\u2030\xa49\right\}.$

Solve for *x*: $5x+8=3x\xe2\u02c6\u201910.$

Solve for $x$: $3\left(2x\xe2\u02c6\u20195\right)\xe2\u02c6\u20193\left(x\xe2\u02c6\u20197\right)=2x\xe2\u02c6\u20199.$

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

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.

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

$\frac{{x}^{2}}{3}\xe2\u02c6\u2019x=-\frac{1}{2}$

Solve: $3x\xe2\u02c6\u20198\xe2\u2030\xa44.$

Solve: $\left|3x\xe2\u02c6\u20192\right|\xe2\u2030\yen 4.$

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

Passes through the points $\left(\xe2\u02c6\u20194,2\right)$ and $\left(5,\mathrm{\xe2\u02c6\u20193}\right).$

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

Passes through the point $\left(2,1\right)$ and is perpendicular to $y=\xe2\u02c6\u2019\frac{2}{5}x+3.$

Add these complex numbers: $(3\xe2\u02c6\u20192i)+(4\xe2\u02c6\u2019i).$

Multiply: $5i\left(5\xe2\u02c6\u20193i\right).$

Solve this quadratic equation and write the two complex roots in $a+bi$ form: ${x}^{2}\xe2\u02c6\u20194x+7=0.$

Solve: ${x}^{2}\xe2\u02c6\u20196x=13.$

Solve: $\sqrt{x\xe2\u02c6\u20197}=x\xe2\u02c6\u20197$

Solve: ${\left(x\xe2\u02c6\u20191\right)}^{\frac{2}{3}}=9$

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

${\left(x+5\right)}^{2}\xe2\u02c6\u20193\left(x+5\right)\xe2\u02c6\u20194=0$