1. Solving Equations

2. An equation links an algebraic expression and a number, or two algebraic expressions with an equals sign. For example: x + 7 = 13 is an equation. In an equation the unknown usually has a particular value. Finding the value of the unknown is called solving the equation. x + 7 = 13 x = 6 When we solve an equation we always line up the equals signs.

3. Using inverse operations to solve equations We can use inverse operations to solve simple equations. For example: x + 5 = 13 x = 13 – 5 x = 8 Always check the solution to an equation by substituting the solution back into the original equation. If we substitute x = 8 back into x + 5 = 13 we have 8 + 5 = 13

4. Using inverse operations to solve equations Solve the following equations using inverse operations. 5 x = 45 x = 45 ÷ 5 x = 9 Check: 5 × 9 = 45 17 – x = 6 17 = 6 + x 17 – 6 = x Check: 17 – 11 = 6 11 = x x = 11 We always write the letter before the equals sign.

5. Using inverse operations to solve equations Solve the following equations using inverse operations. x = 3 × 7 x = 21 Check: 3 x – 4 = 14 3 x = 14 + 4 3 x = 18 Check: 3 × 6 – 4 = 14 x = 18 ÷ 3 x = 6 = 3 x 7 21 7

6. Solving equations by transforming both sides Solve this equation by transforming both sides in the same way: Add 1 to both sides. Multiply both sides by 4. m = 12 We can check the solution by substituting it back into the original equation: 12 ÷ 4 – 1 = 2 – 1 = 2 m 4 = 3 m 4 +1 ×4

7. Constructing an equation Ben and Lucy have the same number of sweets. Ben started with 3 packets of sweets and ate 11 sweets. Lucy started with 2 packets of sweets and ate 3 sweets. How many sweets are there in a packet? Let’s call the number of sweets in a packet, n. We can solve this problem by writing the equation: 3 n – 11 The number of Ben’s sweets = is the same as the number of Lucy’s sweets. 2 n – 3

8. Equations with brackets Equations can contain brackets. For example: 2(3 x – 5) = 4 x To solve this we can Multiply out the brackets: 6x6x –10 = 4 x +10 Add 10 to both sides: 6 x = 4 x + 10 −4 x Subtract 4 x from both sides:2 x = 10 ÷ 2 Divide both sides by 2: x = 5

9. Now try these:

10. Answers: