2.7 Linear inequalities and absolute value inequalities  (Page 7/11)

A man has 72 ft. of fencing to put around a rectangular garden. If the length is 3 times the width, find the dimensions of his garden.

A truck rental is $25 plus $.30/mi. Find out how many miles Ken traveled if his bill was $50.20.

$x^2-5x+9=0$

$2x^2+3x+7=0$

$4-3i$

$\mathrm{-2}-i$

$\left(9-i\right)-\left(4-7i\right)$

$\left(2+3i\right)-\left(-5-8i\right)$

$2\sqrt{-75}+3\sqrt{25}$

$\sqrt{-16}+4\sqrt{-9}$

$-6i(i-5)$

${(3-5i)}^2$

$\sqrt{-4}·\sqrt{-12}$

$\sqrt{-2}\left(\sqrt{-8}-\sqrt{5}\right)$

$\frac{2}{5-3i}$

$\frac{3+7i}{i}$

$2x^2-7x-4=0$

$3x^2+18x+15=0$

$25x^2-9=0$

$7x^2-9x=0$

$x^2=49$

${\left(x-4\right)}^2=36$

$x^2+8x-5=0$

$4x^2+2x-1=0$

$2x^2-5x+1=0$

$15x^2-x-2=0$

${(x-2)}^2=16$

$x^2=10x+3$

$x^{\frac{3}{2}}=27$

$x^{\frac{1}{2}}-4x^{\frac{1}{4}}=0$

$4x^3+8x^2-9x-18=0$

$3x^5-6x^3=0$

$\sqrt{x+9}=x-3$

$\sqrt{3x+7}+\sqrt{x+2}=1$

$\left|3x-7\right|=5$

$\left|2x+3\right|-5=9$

$5x-8\le 12$

$-2x+5>x-7$

$\frac{x-1}{3}+\frac{x+2}{5}\le \frac{3}{5}$

$\left|3x+2\right|+1\le 9$

$\left|5x-1\right|>14$

$\left|x-3\right|<\mathrm{-4}$

$\mathrm{-4}<3x+2\le 18$

$3y<1-2y<5+y$

Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

$\left|x+3\right|\ge 5$

Graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines. See the interval where the inequality is true.

$x+3<3x-4$

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

Find the x- and y -intercepts for the following:

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

$3x-4y=12$

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

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

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

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

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

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.

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

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

Solve: $\left|2x+3\right|<5.$

Solve: $\left|3x-2\right|\ge 4.$

Passes through the points $\left(-4,2\right)$ and $\left(5,\mathrm{-3}\right).$

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 $y=\frac{-2}{5}x+3.$

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

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

Multiply: $5i\left(5-3i\right).$

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

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

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

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

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

Solve:

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

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

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

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

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