1. Chapter 13 Solving Equations

2. Learning Outcomes Solve equations including addition/ subtraction Solve equations including addition/ subtraction Solve equations with multiplication/division Solve equations with multiplication/division Solve mixed equations Solve mixed equations Solve equations with brackets Solve equations with brackets Solve equations with letters on both sides Solve equations with letters on both sides Solve equations with fractions Solve equations with fractions Forming equations and solving Forming equations and solving

3. Solving Equations Going Backwards Examples 1. I think of a number, multiply it by 3 and then subtract 5. The answer is 10. What is my number? 2. To approximately change degrees C to degrees F use double C + 30 (a) Find F when C = 6 (b) Find C when F = 68

4. Example 3. To cook a chicken follow the rule in the box below multiply the weight of the chicken by 40 and then add 20 (a) How long would it take to cook a 3kg chicken? (b) Find the weight of a chicken that took 100 mins

5. Solving Equations A letter term is one with a letter connected to it by multiplying (eg 3x) or dividing ( x / 2 ) A letter term is one with a letter connected to it by multiplying (eg 3x) or dividing ( x / 2 ) Put all letter terms on the left of the equals and all the number terms on the other side of the equals. Put all letter terms on the left of the equals and all the number terms on the other side of the equals. When moving terms to the other side you do the opposite When moving terms to the other side you do the opposite + becomes – - becomes + × becomes ÷ ÷ becomes ×

6. Examples 1. x + 3 = 112. 2p + 1 = 9 3. d – 13 = -54. ¼ t – 1 = 3 5. 4x = 246. 2y + 7 = -3 7. 2b – 5 = 48. -4n = 20 9. 5 – 4n = -110. -6k – 1 = 8 11. ½ x – 7 = -112. 4 / a + 1 = 3 13. 2 – y / 6 = 314. 8d + 4 = 1.6

7. Equations with Brackets Always multiply out the bracket 1 st and then solve as normal Always multiply out the bracket 1 st and then solve as normalExamples 1. 2(x + 3) = 6 2. 3(x + 2) = 12 3. 5(3y – 7) = 25 4. 30 = 5(f + 2) 5. 35 = 5(3p – 10) 6. 3(2t – 3) = 9 7. 5(w – 2) = 7

8. Equations with Letters on Both Sides 1. 3x + 1 = x + 7 2. 3d = 32 – d 3. 3b + 7 = 11 – 3b 4. 2p + 3 = 4 + 5p 5. 4(3 + 2x) = 5(x + 2)

9. Equations with Fractions Remember the bottom of a fraction means divide and the top of a fraction means multiply Remember the bottom of a fraction means divide and the top of a fraction means multiplyExamples 1. 2 / 5 x = 6 2. 3x / 6 = 2 / 5 3. x / 2 + 2x / 3 = 7 4. (x – 1) / 3 = (x + 1) / 4 5. (2x – 3) / 6 + (x + 2) / 3 = 5 / 2

10. Writing Expressions Examples 1. A triangle has sides x cm, (x + 1) cm and (2x – 3) cm. (a) Find an expression for the perimeter] (b) Given that the perimeter is 18cm, find the value of x and hence the 3 sides

11. Examples 2. A birthday party costs £20 plus £5 per person. (a) Find an expression for x people to give the total cost T (b) Jean pays £100 for her birthday. How many people went to the party?

12. Examples 3. A triangle has sides (2t – 1) cm, (2t – 1)cm and (2t – 1) cm. A 2 nd triangle has sides (t + 1) cm, 2t cm and 5 cm. If both triangles have equal perimeters, find the value of t, and hence find the size of sides in both triangles.