Algebra Solving Equations October 2006 ©RSH

Introduction Equations Many people use equations (sometimes without knowing !) A plumber charges £35 for a call out then £17 per hour. If the bill is £69, how long did the job take ? 17x + 35 = 69 That’s the equation. October 2006 ©RSH

Introduction Equations Solving equations means finding the value of the unknown (often written as ‘x’). Some equations are easy to solve by guessing x + 7 = 9 x = 2 Others are not. A set of easy to remember rules will help you to solve ANY equation. October 2006 ©RSH

Notes Equations You can ADD, SUBTRACT, MULTIPLY and DIVIDE both sides of equation by the same number. Do the same thing to both side. October 2006 ©RSH

Notes Example 1 Solve the equation x + 8 = 20 Answer x + 8 = 20 take away 8 x + 8 – 8 = 20 – 8 x = 12 Example 2 Solve the equation x - 8 = 20 Answer x - 8 = 20 add 8 x - 8 + 8 = 20 + 8 x = 28 October 2006 ©RSH

Exercise Solve the following equations x + 5 = 17 x – 12 = 18 October 2006 ©RSH

Notes Harder equations More than one step is usual. You need to solve the harder equations in the Higher Tier. Harder equations More than one step is usual. Write down your method until you get them all right ! Example 3 Solve the equation 2x + 8 = 20 Answer 2x + 8 = 20 take away 8 2x + 8 – 8 = 20 – 8 2x = 12 divide by 2 x = 6 2 2 October 2006 ©RSH

Notes Example 4 Solve the equation 3x - 5 = 28 Answer 3x - 5 = 28 add 5 3x - 5 + 5 = 28 + 5 3x = 33 divide by 3 x = 11 3 3 October 2006 ©RSH

Exercise Solve these equations 3x + 1 = 10 4x + 2 = 22 5x + 3 = 18 October 2006 ©RSH

Notes Equations with Brackets Expand the brackets first and then solve as usual. Example 9 2(x + 1) = 10 2x + 2 = 10 2x = 8 x = 4 Example 10 2(x - 5) = 6 2x - 10 = 6 2x = 16 x = 8 Example 11 2(x - 3)+ 2x = 6 2x - 6 + 2x = 6 4x - 6 = 6 4x = 12 x = 3 October 2006 ©RSH

Exercise Solve these equations 3(x + 1) = 12 4(x – 2) = 20 3x + 3 = 12; 3x = 9; x = 3 4x – 8 = 20; 4x = 28; x = 7 10 + 5x = 25; 5x = 15; x = 3 12x + 6 = 12; 12x = 6; x = ½ 2x – 2 + 3x = 8; 5x – 2 = 8; 5x = 10; x = 2 3x + 3 + 2x + 4 = 14; 5x + 7 = 14; 5x = 7; x = 7/5 4x – 8 –2x – 2 = 10; 2x – 10 = 10; 2x = 20; x = 10 October 2006 ©RSH

Notes Harder again Don’t let the fractions get to you ! Example 5 Solve the equation 3x = 2 Answer divide by 3 It’s fine to Leave your Answer as a Fraction. October 2006 ©RSH

Notes Harder again Don’t let the fractions get to you ! Example 6 Solve the equation Answer multiply by 5 October 2006 ©RSH

Notes Harder again Don’t let the fractions get to you ! Example 7 Solve the equation Answer October 2006 ©RSH

Exercise Solve these equations x = 35 x = 130 3x = 18; x = 6 5x = -24; x = -24/5 or –4.8 October 2006 ©RSH

Notes Harder again Step by step Answer Example 8 Solve the equation October 2006 ©RSH

Exercise Solve these equations x/5 = 6; x = 30 x/2 = 5; x = 10 October 2006 ©RSH

Notes …and finally What happens if there is an x on both sides. Re-arrange to get all the x’s on one side and numbers on the other. Example 12 Solve 3x + 1 = x + 3 Answer 3x + 1 = x + 3 subtract 1 3x + 1 – 1 = x + 3 – 1 3x = x + 2 3x – x = x – x + 2 subtract x 2x = 2 divide by 2 x = 1 October 2006 ©RSH

Exercise Solve these equations 3x + 7 = x – 3 5x – 5 = 7 – x 5x = 12; x = 12/5 or 2.4 x = -7 14 = 4x; 4x = 14; x = 3.5 October 2006 ©RSH