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Algebra Solving Equations October 2006 ©RSH

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**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

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**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 = x = 2 Others are not. A set of easy to remember rules will help you to solve ANY equation. October 2006 ©RSH

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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

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**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 = x = 28 October 2006 ©RSH

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**Exercise Solve the following equations x + 5 = 17 x – 12 = 18**

October 2006 ©RSH

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**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

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**Notes Example 4 Solve the equation 3x - 5 = 28 Answer**

3x - 5 = 28 add 5 3x = 3x = 33 divide by 3 x = 11 3 3 October 2006 ©RSH

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**Exercise Solve these equations 3x + 1 = 10 4x + 2 = 22 5x + 3 = 18**

October 2006 ©RSH

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**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 x = 6 4x - 6 = 6 4x = 12 x = 3 October 2006 ©RSH

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**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 x + 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

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**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

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**Notes Harder again Don’t let the fractions get to you ! Example 6**

Solve the equation Answer multiply by 5 October 2006 ©RSH

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**Notes Harder again Don’t let the fractions get to you ! Example 7**

Solve the equation Answer October 2006 ©RSH

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**Exercise Solve these equations x = 35 x = 130 3x = 18; x = 6**

5x = -24; x = -24/5 or –4.8 October 2006 ©RSH

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**Notes Harder again Step by step Answer Example 8 Solve the equation**

October 2006 ©RSH

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**Exercise Solve these equations x/5 = 6; x = 30 x/2 = 5; x = 10**

October 2006 ©RSH

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**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

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**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

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