Issuu on Google+

How To Solve Absolute Value Equations How To Solve Absolute Value Equations Learn absolute value equations concept. The equation |x| = 4. This means that x could be 4 or x could be -4. When you take the absolute value of 4, the solution is 4 and when you take the absolute value of -4, the solution is also 4. An absolute value problem, you have to get into account that there can be two solutions that will make the equation true. Learning absolute value equation, you set the quantity inside the absolute value symbol equal to the positive and negative value on the other side of the equal symbol. Solve Absolute Value Equations Below are the examples on how to solve absolute value equations Example 1 : -|x + 1| = 4 Solution : The quantity inside the absolute value symbol can be equal to 4 or -4 x + 1 = 4 or x + 1 = - 4 Subtract 1 on both side of the given equation x + 1 - 1 = 4 - 1 or x + 1 - 1 = -4 - 1 x = 3 or x = -5 Know More About Polynomial Factoring

Math.Tutorvista.com

Page No. :- 1/5


So the solution are x = 3 and x = -5 Example 2 : |2x - 3| = x - 5 Solution : When solving this equation, you have to be careful when solving opposite of (x - 5) 2x - 3 = x - 5 or 2x - 3 = -(x - 5) x - 3 = -5 or 2x -3 = -x + 5 x = -2 or 3x – 3 = 5 3x = 8 x= So, the solution is x = -2 and x = 83 Example 3 : |x + 1| = 5 Solution : The quantity inside the absolute value symbol can be equal to 5 or -5 x + 1 = 5 or x + 1 = -5 Subtract 1 on both side of the given equation x + 1 - 1 = 5 - 1 or x + 1 - 1 = - 5 - 1 x = 4 or x = - 6 So the solution are x = 4 and x = - 6 Absolute Value Equations Practice ProblemsBack to Top Problem 1: |x + 1| = 6 Problem 2: |x + 1| = 7 Solve absolute value equations – answer key: Problem 1: x = 5 and x = -7 Problem 2: x = 6 and x = -8

Math.Tutorvista.com

Learn More Transitive Property of Equality

Page No. :- 2/5


Linear Combination Linear Combination Linear combination is combination of two lines. Linear combination is also called as addition method. Linear combination is one of the methods to solve system of two equations. By this method, we can solve the variable x and y. Steps for solving systems of equation using linear combination method: We need to add two line equations for eliminating any one variable. Then we get a new equation of one variable. Solve this, we get a value of that variable. Substitute this variable value into any one original equation, we get a value for another variable. Let us see about how to solve linear equations using linear combination method. Solving Linear Combination Below you could see examples for solving linear combination Example 1: Solving the linear equations using linear combination method. 7X - y = 5 and 2x + 3y = 8 Math.Tutorvista.com

Page No. :- 3/5


Solution : The given equations are 7X - y = 5 (1) 2x + 3y = 8 (2) Multiply by 3 to the equation (1) 21x - 3y = 15 Multiply by 1 to the equation (2) 2x + 3y = 8 Add both these equations. 21x - 3y + (2x + 3y) = 15 + 8 21x - 3y + 2x + 3y = 15 + 8 Combine like terms. 21x + 2x - 3y + 3y = 23 23x = 23 Isolate the variable x. X=1 Substitute the value of x variable into the equation (2) 2X + 3y = 8 2(1) + 3y = 8 2 + 3y = 8 Subtract 2 from each side. 2 - 2 + 3y = 8 - 2 3y = 6 Read More About Word Problems Algebra

Math.Tutorvista.com

Page No. :- 4/5


Thank You

Math.TutorVista.com


How To Solve Absolute Value Equations