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Solving for x December 7, 2010 Solving for x • When solving an equation, the goal is to get the variable by itself on one side of the equation. • Inverse operations are the same as opposite operations. • Addition and subtraction are inverse operations. • Multiplication and division are inverse operations. Solving for x • variable term – the term containing a variable. • number term – the term containing only a number. • If the number term is positive, subtract it from both sides of the equation. • If the number term is negative, add its positive value to both sides of the equation. One-Step Equations • A one-step equation is as straightforward as it sounds. You will only need to perform one step in order to solve the equation. One-Step Equations • One goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other goal is to have the number in front of the variable equal to one. One-Step Equations • Solve x + 5 = -17 • Subtract 5 from both sides, or flip 5 to the other side. Subtract Flip x + 5 = -17 x + 5 = -17 -5 -5 x = -17 - 5 x = -22 x = -22 Two-Step Equations • A two-step equation is as straightforward as it sounds. You will need to perform two steps in order to solve the equation. • In solving two-step equations you will make use of the same techniques used in solving one-step equation only you will perform two operations rather than just one. Two-Step Equations • Solve 3x + 4 = 13 Subtract 3x + 4 = 13 - 4 -4 3x = 9 3 3 x=3 Flip 3x + 4 = 13 3x = 13 - 4 3x = 9 3 3 x=3 Two-Step Review • Move the number term by either adding it or subtracting it on both sides of the equation. • Move the coefficient by dividing by the coefficient on both sides of the equation. Multi-Step Equations • In multi-step equations, you will need to make use of the techniques used in solving one-step and two-step equations. • Just as with solving one-step or two-step or any equation, one goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other goal is to have the number in front of the variable equal to one. Keep in mind that the variable does not always have to be x. These equations can make use of any letter as a variable. Multi-Step Equations • Solve 4x + 9 = 2x – 5 Subtract 4x + 9 = 2x – 5 -2x -2x 2x + 9 = -5 -9 -9 2x = -14 2 2 x = -7 Flip 4x + 9 = 2x - 5 4x – 2x + 9 = -5 2x + 9 = -5 2x = -5 – 9 2x = -14 2 2 x = -7 Multi-Step Review • Combine like terms on each side. • Get the variable terms on the same side of the equation. – Add or subtract the one variable term to get it to the side of the variable term with the larger coefficient. • Move the number term by adding or subtracting. – Add if the number term is negative. – Subtract if the number term is positive • Move the coefficient by dividing. • If the variable terms cancel on both sides the answer is no solution. • If all terms and coefficients cancel on both sides (nothing is left), the answer is any number.