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

 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. 84 mi ## Complex Numbers For the following exercises, use the quadratic equation to solve. ${x}^{2}-5x+9=0$ $2{x}^{2}+3x+7=0$ $x=\frac{-3}{4}±\frac{i\sqrt{47}}{4}$ For the following exercises, name the horizontal component and the vertical component. $4-3i$ $-2-i$ horizontal component $\text{\hspace{0.17em}}-2;$ vertical component $\text{\hspace{0.17em}}-1$ For the following exercises, perform the operations indicated. $\left(9-i\right)-\left(4-7i\right)$ $\left(2+3i\right)-\left(-5-8i\right)$ $7+11i$ $2\sqrt{-75}+3\sqrt{25}$ $\sqrt{-16}+4\sqrt{-9}$ $16i$ $-6i\left(i-5\right)$ ${\left(3-5i\right)}^{2}$ $-16-30i$ $\sqrt{-4}·\sqrt{-12}$ $\sqrt{-2}\left(\sqrt{-8}-\sqrt{5}\right)$ $-4-i\sqrt{10}$ $\frac{2}{5-3i}$ $\frac{3+7i}{i}$ $x=7-3i$ ## Quadratic Equations For the following exercises, solve the quadratic equation by factoring. $2{x}^{2}-7x-4=0$ $3{x}^{2}+18x+15=0$ $x=-1,-5$ $x=0,\frac{9}{7}$ For the following exercises, solve the quadratic equation by using the square-root property. ${x}^{2}=49$ ${\left(x-4\right)}^{2}=36$ $x=10,-2$ For the following exercises, solve the quadratic equation by completing the square. ${x}^{2}+8x-5=0$ $4{x}^{2}+2x-1=0$ $x=\frac{-1±\sqrt{5}}{4}$ For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No real solution . $2{x}^{2}-5x+1=0$ $15{x}^{2}-x-2=0$ $x=\frac{2}{5},\frac{-1}{3}$ For the following exercises, solve the quadratic equation by the method of your choice. ${\left(x-2\right)}^{2}=16$ ${x}^{2}=10x+3$ $x=5±2\sqrt{7}$ ## Other Types of Equations For the following exercises, solve the equations. ${x}^{\frac{3}{2}}=27$ ${x}^{\frac{1}{2}}-4{x}^{\frac{1}{4}}=0$ $x=0,256$ $4{x}^{3}+8{x}^{2}-9x-18=0$ $3{x}^{5}-6{x}^{3}=0$ $x=0,±\sqrt{2}$ $\sqrt{x+9}=x-3$ $\sqrt{3x+7}+\sqrt{x+2}=1$ $x=-2$ $|3x-7|=5$ $|2x+3|-5=9$ $x=\frac{11}{2},\frac{-17}{2}$ ## Linear Inequalities and Absolute Value Inequalities For the following exercises, solve the inequality. Write your final answer in interval notation. $5x-8\le 12$ $-2x+5>x-7$ $\left(-\infty ,4\right)$ $\frac{x-1}{3}+\frac{x+2}{5}\le \frac{3}{5}$ $|3x+2|+1\le 9$ $\left[\frac{-10}{3},2\right]$ $|5x-1|>14$ $|x-3|<-4$ No solution For the following exercises, solve the compound inequality. Write your answer in interval notation. $-4<3x+2\le 18$ $3y<1-2y<5+y$ $\left(-\frac{4}{3},\frac{1}{5}\right)$ For the following exercises, graph as described. 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. $|x+3|\ge 5$ 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. $x+3<3x-4$ Where the blue is below the orange line; point of intersection is $\text{\hspace{0.17em}}x=3.5.$ $\left(3.5,\infty \right)$ ## Chapter practice test Graph the following: $\text{\hspace{0.17em}}2y=3x+4.$ $y=\frac{3}{2}x+2$ x y 0 2 2 5 4 8 Find the x- and y -intercepts for the following: $2x-5y=6$ Find the x- and y -intercepts of this equation, and sketch the graph of the line using just the intercepts plotted. $3x-4y=12$ $\left(0,-3\right)$ $\left(4,0\right)$ Find the exact distance between $\text{\hspace{0.17em}}\left(5,-3\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(-2,8\right).\text{\hspace{0.17em}}$ 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 $\text{\hspace{0.17em}}\left\{x|x\le 9\right\}.$ $\left(-\infty ,9\right]$ Solve for x : $\text{\hspace{0.17em}}5x+8=3x-10.$ Solve for x : $\text{\hspace{0.17em}}3\left(2x-5\right)-3\left(x-7\right)=2x-9.$ $x=-15$ Solve for x : $\text{\hspace{0.17em}}\frac{x}{2}+1=\frac{4}{x}$ Solve for x : $\text{\hspace{0.17em}}\frac{5}{x+4}=4+\frac{3}{x-2}.$ $x\ne -4,2;$ $x=\frac{-5}{2},1$ 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. $\frac{{x}^{2}}{3}-x=\frac{-1}{2}$ $x=\frac{3±\sqrt{3}}{2}$ Solve: $\text{\hspace{0.17em}}3x-8\le 4.$ Solve: $\text{\hspace{0.17em}}|2x+3|<5.$ $\left(-4,1\right)$ Solve: $\text{\hspace{0.17em}}|3x-2|\ge 4.$ For the following exercises, find the equation of the line with the given information. Passes through the points $\text{\hspace{0.17em}}\left(-4,2\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(5,-3\right).$ $y=\frac{-5}{9}x-\frac{2}{9}$ Has an undefined slope and passes through the point $\text{\hspace{0.17em}}\left(4,3\right).$ Passes through the point $\text{\hspace{0.17em}}\left(2,1\right)\text{\hspace{0.17em}}$ and is perpendicular to $\text{\hspace{0.17em}}y=\frac{-2}{5}x+3.$ $y=\frac{5}{2}x-4$ Add these complex numbers: $\text{\hspace{0.17em}}\left(3-2i\right)+\left(4-i\right).$ Simplify: $\text{\hspace{0.17em}}\sqrt{-4}+3\sqrt{-16}.$ $14i$ Multiply: $\text{\hspace{0.17em}}5i\left(5-3i\right).$ Divide: $\text{\hspace{0.17em}}\frac{4-i}{2+3i}.$ $\frac{5}{13}-\frac{14}{13}i$ Solve this quadratic equation and write the two complex roots in $\text{\hspace{0.17em}}a+bi\text{\hspace{0.17em}}$ form: $\text{\hspace{0.17em}}{x}^{2}-4x+7=0.$ Solve: $\text{\hspace{0.17em}}{\left(3x-1\right)}^{2}-1=24.$ $x=2,\frac{-4}{3}$ Solve: $\text{\hspace{0.17em}}{x}^{2}-6x=13.$ Solve: $\text{\hspace{0.17em}}4{x}^{2}-4x-1=0$ $x=\frac{1}{2}±\frac{\sqrt{2}}{2}$ Solve: $\sqrt{x-7}=x-7$ Solve: $\text{\hspace{0.17em}}2+\sqrt{12-2x}=x$ $4$ Solve: $\text{\hspace{0.17em}}{\left(x-1\right)}^{\frac{2}{3}}=9$ For the following exercises, find the real solutions of each equation by factoring. $2{x}^{3}-{x}^{2}-8x+4=0$ $x=\frac{1}{2},2,-2$ ${\left(x+5\right)}^{2}-3\left(x+5\right)-4=0$ #### Questions & Answers how do I set up the problem? Harshika Reply what is a solution set? Harshika find the subring of gaussian integers? Rofiqul hello, I am happy to help! Shirley Reply please can go further on polynomials quadratic Abdullahi hi mam Mark I need quadratic equation link to Alpa Beta Abdullahi Reply find the value of 2x=32 Felix Reply divide by 2 on each side of the equal sign to solve for x corri X=16 Michael Want to review on complex number 1.What are complex number 2.How to solve complex number problems. Beyan yes i wantt to review Mark use the y -intercept and slope to sketch the graph of the equation y=6x Only Reply how do we prove the quadratic formular Seidu Reply please help me prove quadratic formula Darius hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher Shirley Reply thank you help me with how to prove the quadratic equation Seidu may God blessed u for that. Please I want u to help me in sets. Opoku what is math number Tric Reply 4 Trista x-2y+3z=-3 2x-y+z=7 -x+3y-z=6 Sidiki Reply can you teacch how to solve that🙏 Mark Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411 Brenna (61/11,41/11,−4/11) Brenna x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11 Brenna Need help solving this problem (2/7)^-2 Simone Reply x+2y-z=7 Sidiki what is the coefficient of -4× Mehri Reply -1 Shedrak the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1 Alfred Reply An investment account was opened with an initial deposit of$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation By By By OpenStax By George Turner By OpenStax By By Karen Gowdey By Danielle Stephens By OpenStax By Heather McAvoy By Jonathan Long By OpenStax