Solving inequalities kuta of Technology
©l R2J0 G1c2x sK vu Xt1a9 MS9o hf AtMwNaHr5e W 1L vLYCe.b A 6A MlPlk LrXiCg dhPtdsw Mrle EsRejr ovQeMdf. k e IM9aUdceY HwOiht fh s DIEnZfiBnnintrev lP 0rner-eA ylLguedbkr 1aX.0 Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Inequalities and Their Graphs Date_____ Period____Solving Two-Step Inequalities KUTA.pdf Author: STONERK Created Date: 11/5/2012 5:06:57 PM ...21) Write an inequality with x on both sides whose solution is x ≥ 2 Many answers. Ex: 2x ≥ x + 2 22) Name one particular solution to question #20. Any number greater than zero. Ex: 4.7-2-Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com First, let us clear out the "/3" by multiplying each part by 3. Because we are multiplying by a positive number, the inequalities don't change: −6 < 6−2x < 12. Now subtract 6 from each part: −12 < −2x < 6. Now divide each part by 2 (a positive number, so again the inequalities don't change): −6 < −x < 3.Whether you love math or suffer through every single problem, there are plenty of resources to help you solve math equations. Skip the tutor and log on to load these awesome websites for a fantastic free equation solver or simply to find an...©O c2l0 7102y LK Iu lt 9aC dS Moaf WtswaNryee WLWLGC1.d 4 qAxlOl6 Frfi tg HhdtIsv Ir7e yseGrEvje 2d a.U m jMhaKd0e1 JwPiCt whD rI nlfai HnSirtUeH NA8l og oeTb urXaQ l1 X.i Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Solving Systems of Inequalities Date_____ Period____Vertex form. Graphing quadratic inequalities. Factoring quadratic expressions. Solving quadratic equations w/ square roots. Solving quadratic equations by factoring. Completing the square. Solving equations by completing the square. Solving equations with the quadratic formula. The discriminant. Vertex form. Graphing quadratic inequalities. Factoring quadratic expressions. Solving quadratic equations w/ square roots. Solving quadratic equations by factoring. Completing the square. Solving equations by completing the square. Solving equations with the quadratic formula. The discriminant. ©x Y2k0f1_8w RKButtCaB ZSrozfHtAwGa_rYeu rLELPCf.C y RALlPlI CrhiogKhptcse krOeosdeGrFvQewdJ.J z JMDaxdDeU NwDistQha GIXnPfdiXnLi]tleT ]Aulqg`ebbwrRau Z1z.R o 3AwlvlR 1r Si Ogdh WtasW Crge Ns1evruvce nd w.6 X 5M ma cdhe M 6w Ei Jt jh a eIWn7f3iQn ZiGt ne7 tP Fr1eZ-GATlmgIedbtr 0ai. 8 Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Solving One-Step Inequalities by Adding/Subtracting Date_____ Period____ Solve each equation for the indicated variable. 1) g x , for x 2) u x , for x 3) z m x , for x 4) g ca , for a©a K2r0 E1Y2K PK 3u2t6ak QSto 5fRtAwca BrJe l RLbLyCT.R 4 TA ClHlX brFiSgYhdt Vsu 5rLeXs se Nrbv ePd W.s j uM Wavd 4ed qw Ci Utsh L 9I qnbf aiNnkiNtzeK lA Plug TeMbxrka 4 q1x. 2 Worksheet by Kuta Software LLC Infinite Algebra 1 Name_____ One-Step Inequalities Date_____ Period____ ©r h2g0 S1X1y jK euhtTag bSPoof vt7w 2aRr8e c GLcL qC D.0 i zA Ll nl y NrqiBgQhDtts8 frre Ksce r8v depdG.H I qM aAdKev 5w Fi OtHhY jI rn1f1i mnai 7t Ge6 0A8l ag DeObzr vaO f2H.y Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Solving Rational Equations Date_____ Period____©L B2Q0A1Y1c lK nu 0tTa v 6SVohfEt vwvabrre O HLbL 9CT. o G tA LlMl1 hr1i fg 1hFt Lsv XrCeAsOe7r jvieZdK.V D 1M 6a 7d Dej 1wti 1t QhQ vIntf yi Dn5i qt 5e6 CAEl5g Pejb ur Xad 82Y.Q Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Solving Inequalities Date_____ Period____ J L VA1l Wlm Sr9i qgZh8t Us3 Nrze4sFepr IvWeIdw.Z h qM 0a id te P rwoi8tih R hIOn7f jiPnUi2t e6 4AJlUg6e1bArca h i16. C Worksheet by Kuta Software LLC 13) x 14) a 15) x 16) x 17) b 18) b Write an inequality for each graph. 19)This Inequality Worksheet will create a handout for the properties of inequalities. It explains the inequalities symbols, and graphing symbols with examples. This Inequality handout is a good resource for students in the 5th Grade through the 8th Grade. These Inequality Worksheets will produce problems for graphing single variable inequalities.Solve each equation, if possible. If there is no solution, write "no solution"; if it is the identity situation, write "all real numbers". 1) 7 m − 7 − 6m − 16 = 1 + 4m {−8} 2) 3 + 4n + n = 2n + 15 {4} 3) 11 + 2p = p + 4 {−7} 4) −7k − 4k = 8 − 2k − 8k {−8} 5) −5 + 5(n − 7) = −40 + 5n { All real numbers. } 6) 8k − 6 ...©m Z2 y0R152 W vKlu ot2a z YSnovf 8tcw Za zr re 0 tL uL 1C A.l q lA HlXlk ir piMgKhPtIs f 0r2e 9s9e5rTvue WdU.3 G UMna4d ieM jw 6iZt shp dI fnsf oiSnBi4t 0e5 qAPlKgIe kb Irja m 92K.6 Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Compound Inequalities Date_____ Period____ ©J a2]0e1H8a HKhuKtqa] wSNo`fetdwwa^rjet ILWLTCq.q ` IAclqlf Lr[itgkhFtGsx Wrteysbeurrvuehdl.s R aMKaGdxeH qwyietnhM wIbnTfWixnUi]tjea cAtlHgHe\b]rBaT e1W.In this explainer, we will be focusing on quadratic inequalities. This is in contrast to linear inequalities, which look something similar to the following: − 2 𝑥 + 3 ≤ 5. Recall that the procedure to solve inequalities of this form is quite straightforward. The first thing we want to do is rearrange the inequality so all of the 𝑥 ...Interval notation: ( − ∞, 3) Any real number less than 3 in the shaded region on the number line will satisfy at least one of the two given inequalities. Example 2.7.4. Graph and give the interval notation equivalent: x < 3 or x ≥ − 1. Solution: Both solution sets are graphed above the union, which is graphed below.Systems of Inequalities Sketch the solution to each system of inequalities. y > 4 x − 3 Date________________ Period____ 2) y ≥ −5 x + 3 ≥ −2 x + 3 5 4 3 2 −5 −4 −3 −2 −1 0 −1 −2 −3 −4 −5 3) y < 3 ≤ − x + 1 5 4 3 2 −5 −4 −3 −2 −1 0 −1 −2 −3 −4 −5 2 2 3 4 3 4 5 5 Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com.X 1 RMva 3dQeI 7wIi it hS iI 3nUfPiQn0iMt1eC APorMem-GA6l yg3e mbor ca9. j Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Solving One-Step Inequalities by Multiplying/Dividing Date_____ Period____ Solve each inequality and graph its solution. 1) −5 x ≥ 25Create your own worksheets like this one with Infinite Pre-Algebra. Free trial available at KutaSoftware.com.21) Explain two ways you could solve 20 = 5(−3 + x) -2- ©D 72 g061 U1Y 5K Uu Ptxat nSTozfHtKw4aDr Fe y yLzLpCJ. j j uA xl Fl H frzi Ngvh ntwsf 9r Desje Lrmv3eGdj. g b gM da gdke N Lw6ixtWhX CIenWf4i on Pijt1e L TAHlWgfe rb UrTa0 m2O.b Worksheet by …11) Write a polynomial inequality with the solution: { }∪{ }∪[ , ) Example: (x ) (x ) (x ) Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com©L B2Q0A1Y1c lK nu 0tTa v 6SVohfEt vwvabrre O HLbL 9CT. o G tA LlMl1 hr1i fg 1hFt Lsv XrCeAsOe7r jvieZdK.V D 1M 6a 7d Dej 1wti 1t QhQ vIntf yi Dn5i qt 5e6 CAEl5g Pejb ur Xad 82Y.Q Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Solving Inequalities Date_____ Period____ Test and Worksheet Generator for Algebra 2. Infinite Algebra 2 covers all typical Algebra 2 material, beginning with a few major Algebra 1 concepts and going through trigonometry. There are over 125 topics in all, from multi-step equations to trigonometric identities. Suitable for any class with advanced algebra content.©p 32e0 Q1j2Z QKAuMtHa9 tSToxf8t MwVapr peQ 5LZLQC 0.H Z RABlble jr2i jg eh2t rs K Pr0e OsBegrcv6eWd9. k s RMja cd hel MwWivt Hh8 gIjn Xfai 9nBi5tBe B HPGrae j- eAOl7g 6eRbkroa S.9 Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ Solving Two-Step Inequalities Date_____ Period____Software for math teachers that creates custom worksheets in a matter of minutes. Try for free. Available for Pre-Algebra, Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus.Interval notation: ( − ∞, 3) Any real number less than 3 in the shaded region on the number line will satisfy at least one of the two given inequalities. Example 2.7.4. Graph and give the interval notation equivalent: x < 3 or x ≥ − 1. Solution: Both solution sets are graphed above the union, which is graphed below.Y j QMSaed ReH 2wXiqt thx NI1n PfBi 7n LiutUey ZA dl 3g Leib MrsaC 61 b.y Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Solving Systems of Equations by Elimination Date_____ Period____ Solve each system by elimination. 1) −4 x − 2y = −12 4x + 8y = −24 2) 4x + 8y = 20©D p2R0N112 H bK RuDt Sar 0SuoUfDtvw8aar 8em tL xL FCY.s D cAXlMl3 xr AipgOh StWsI XrUexs Vesrlv Ne2d y.h y aMGaDdPej Dwxiht Ih E PI sn3f WiYnAixt Qey oA FlVg6e vbEr QaH E1C.p Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Graphing Linear Inequalities Date_____ Period____Triangles. Medians of triangles. Altitudes of triangles. Angle bisectors. Circles. Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format.©j f2 20H1t2 d RKUuMtqa0 FS vo bfjt 9wta or qe5 zL QLIC G.c X 3AFlEl6 9r8ivg9h ntJsm hr Be Js 0e Qr9vCeid H.9 h HMJaJd ex iw qiIt phS IXncfYitn 1iBtueY kP 3r JeS- vAalJgje 7b Hra8.k Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____ The Distributive Property Date_____ Period____Solving Basic Linear Equations. An equation 129 is a statement indicating that two algebraic expressions are equal. A linear equation with one variable 130, \(x\), is an equation that can be written in the standard form \(ax + b = 0\) where \(a\) and \(b\) are real numbers and \(a ≠ 0\).For example \(3 x - 12 = 0\) A solution 131 to a linear equation is …Solving systems of equations by graphing; Solving systems of equations by elimination; Solving systems of equations by substitution; Systems of equations word problems; …Solving inequalities. Do excercises Show all 3 exercises. Solving inequalities I. Solving inequalities II. Solving inequalities III. When we add or subtract the same number on both sides of the truth of the inequality doesn't change. This holds true for all numbers: x > y → x < y →. x + z > y + z → x + z < y + z →.Kuta Software - Infinite Algebra 1 Name_____ Graphing Linear Inequalities Date_____ Period____ Sketch the graph of each linear inequality.21) Write an inequality with x on both sides whose solution is x ≥ 2 Many answers. Ex: 2x ≥ x + 2 22) Name one particular solution to question #20. Any number greater than zero. Ex: 4.7-2-Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com©F E2Z0k1 v2c MKQuOthaM tS go vfWtLw Sa zroe D RLoL KC2. I G A4lHlY QrEi AgNhEtWsR frve cs oe 8rJv decd2.D S 6M 7a rd Weg qwpiNtkhE yI bnEfLi Pnui GtQem xA XlcgYeibzr Pay 82 b.j Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Quadratic Inequalities Date_____ Period____Math homework can often be a challenging task, especially when faced with complex problems that seem daunting at first glance. However, with the right approach and problem-solving techniques, you can break down these problems into manageabl...A L 1Mda9d keN 6wsi rt 4hw HINnbf Ti7n niPt ie2 uAjlagte 8b 0r4aL Y1e.E Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 1 Name_____ Compound Inequalities Date_____ Period____ Solve each compound inequality and graph its solution. 1) m or mSolving a System of Nonlinear Equations Using Substitution. A system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear. Recall that a linear equation can take the form Ax + By + C = 0. A x + B y + C = 0. Any equation that cannot be written in this form in ...The magazine cost $4. Solve the inequality to find the maximum cost of each composition book. 4) Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27. Solve the inequality to find the maximum number of hours Amanda rented the bike. 5) You need to buy some pencils and an eraser.©M 12 r0F1 328 PKru rtoa n uSko afDt8w Ea grje z 4L rL cC x.S u aA pljl 8 Or8i qgOhUtBsa HrMezsseDr1vBe1di. 7 O UMwaDdNeO 0w ViGt0h 7 vI PnmfPi Ln6i tReR oPfr yeF- LAAlWgYefb Lrra A.u Worksheet by Kuta Software LLC Kuta Software - Infinite Pre-Algebra Name_____Test and Worksheet Generator for Pre-Algebra. Infinite Pre-Algebra covers all typical Pre-Algebra material, over 90 topics in all, from arithmetic to equations to polynomials. Suitable for any class which is a first step from arithmetic to algebra. Designed for all levels of learners from remedial to advanced. Integers, Decimals, and Fractions.Worksheet by Kuta Software LLC Week 5 Day 5 1.5: Graphing Linear Inequalities & Solving Systems (review) Name_____ Period____ ©j j2X0S2y0M IKsuPtXa[ \SXoFfltjwuakrKeq rLBLOCN.W Z KAClnlf XrOiRgEhBtwsI Oree`sqeHr`vleDdy.-1-Sketch the graph of each linear inequality. Let's do these together. 1) y ³ x - 2 x y-6-5-4-3-2-1123456Y a pA tllT 9rXilg0h Ltps 5 rne0svelr qv5efd P.S 8 6M Ia7dAeM qwrilt ghG MIonif ziin PiWtXe y qAtl 8g keFb 9ruaS T2P.T Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Solving Systems of Three Equations w/ Elimination Date_____ Period____ Solve each system by elimination. 1) −Solving Quadratic Inequalities Name___________________________________ Solve the quadratic inequality. Show all of your work on your own paper. 1) x2− 3x≤ 0 2) 9 −x2< 0 3) −2x2+ 3x+ 5 ≤ 0 4) x2− 5 > 4xFree worksheet at https://www.kutasoftware.com/free.htmlGo to ️ https://maemap.com/math/algebra1/ ⬅️ for more Algebra 1 information!Please support …21) Explain two ways you could solve 20 = 5(−3 + x) -2- ©D 72 g061 U1Y 5K Uu Ptxat nSTozfHtKw4aDr Fe y yLzLpCJ. j j uA xl Fl H frzi Ngvh ntwsf 9r Desje Lrmv3eGdj. g b gM da gdke N Lw6ixtWhX CIenWf4i on Pijt1e L TAHlWgfe rb UrTa0 m2O.b Worksheet by …©j M230g1 q1C QK8uWtKaB CSQovfWt0w ka9r TeY 0LlLFCg.1 m WAIlFlT hrhisgRhTtRsz Yr2eLsAemrnvPe Sdg. 6 0 nMnaad5e C Lwji Xtyhr rIZn QfJiOnKiHtRe9 4A 4l cg iepbCrAaX p2 a.H Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name_____ Systems of Inequalities Date_____ Period____ Free worksheet at https://www.kutasoftware.com/free.htmlGo to ️ https://maemap.com/math/algebra1/ ⬅️ for more Algebra 1 information!Please support … ©l R2J0 G1c2x sK vu Xt1a9 MS9o hf AtMwNaHrWorksheet by Kuta Software LLC Algebra 1/Jackson SyFree Algebra 1 worksheets created with Infinite Alg
