PPT-Hardness of Approximately Solving Linear Equations Over

Reals Dana Moshkovitz MIT Joint work with Subhash Khot NYU We propose an approach for proving the unique games conjecture by studying the hardness of approximately solving real. Lesson Objective:. An equation is like a set of scales.. To keep it balanced, whatever you. do to one side you must do to the other.. Use this idea to solve equations like:. 3x + 1 = x + 7 . 2 (3x + 1) = 3 (x – 2). . 1. Label the two beakers with their respective names. . 2. Put 10 . mL. of sample in their respective beakers.. . 3. Dip one test strip in sample beaker for 3 seconds.. . 4. Remove and immediately match to the closest . For . example:. Could . you tell that the . equations . y=2x +1 and y= 2x-7 . have . no . solution?. In this lesson you . will learn to predict how many solutions a system of linear equations has . by inspection.. What is Hardness. ?. Hardness is a mineral’s ability to scratch something or be scratched. Some minerals are extremely soft and can be scratched by your fingernail and some minerals can scratch glass or metal.. By:. Emily Zhou. What is a Linear Equation?. A linear equation is an equation whose graph forms a straight line.. Linear equations are usually shown on a coordinate plane. Real life situations of linear equations include the stock market as well as the payments of a car.. Problem 1. There are 25 toys in a playground. . The toys are either bicycles (2 wheels) or tricycles (3 wheels). . In total in the playground there are 61 wheels. . How many bicycles are in the playground?. • Resistance to permanently indenting the surface.. • Large hardness means:. --resistance to plastic deformation or cracking in. compression.. --better wear properties.. e.g., . Mathematical Language. A . solution. of an equation is a number that make the equation true. 3x+2=17. To . solve. an equation means to find all its solution. Two equations are equivalent if they have the same solutions. If you read from left to right . 10 . “is greater than “ . 5. . X. If you read from right to left . 5. . “is less than “ . 10. . X. If you read from left to right . 5. . “is less than “ . Only those with single-step equation experience dare proceed!. Section 6.4. Equation Solving. When we solve equations, our goal is to find the . _______. . of the . variable. ; the . _________. . to the equation. . 2. 8.1: First Order Systems. We now look at systems of linear differential equations.. One of the main reasons is that any nth order differential equation with n > 1 can be written as a first order system of n equations in n unknown functions.. What we will learn. Solve linear equations using addition and subtraction. Solve linear equations using multiplication and division. Use linear equations to solve real-life problems. Needed Vocab. Equation:. Clayton County Summer Math Academy. Algebra I – Solving Equations & Systems. Sarah Ledford. June 9, 2015. 1. Solve it!. 2. Solve the following equation for . t. :. 105 = 100(1 + .05. t. ). Explain how you solved it & how you know your solution is correct. . Presented by Willrich Precision. Ph 866-945-5742 / sales@Willrich.com. Created by Walter . Wardzala. , Major Instrument Sales Specialist. . Materials Testing. Tensile. Charpy. Impact. Fatigue. Ductility.