1. Algebra
Solving Equations
October 2006
©RSH

2. 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

3. 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

4. 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

5. 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

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

7. 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

8. 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

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

10. 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

11. 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

12. 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

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

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

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

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

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

18. 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

19. 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