SOLVING LINEAR EQUATIONS

Example 1 Solve take 3 from both sides divide both sides by 2

Example 2 Solve add 2 to both sides divide both sides by 3

Example 3 Solve take 4x from both sides add 2 to both sides expand the brackets divide both sides by 2

Example 4 Solve take 4x from both sides add 12 to both sides expand the brackets divide both sides by 8

Example 5 Solve simplify take 7 from both sides expand the brackets divide both sides by 4

Example 5 Solve add 5 to both sides divide both sides by 10 add 3x to both sides

Example 6 Solve simplify add 2x to both sides expand the brackets add 7 to both sides divide both sides by 5

Example 7 The three angles of the triangle are shown in terms of x. a Find the value of x. b Write down the size of each angle in the triangle. take 114 from both sides divide both sides by 3 simplify a b NOT TO SCALE Angles are: 130 o, 4 o and 46 o

Example 8 Find the length of a side of this square. All lengths are in cm. take 4x from both sides add 4 to both sides expand the brackets divide both sides by 2 Length of side =

Example 9 Find the length of the rectangle. All lengths are in cm. add 15x to both sides add 9 to both sides expand the brackets divide both sides by 2 Length of rectangle =

Example 10 Expression A is 7 more than expression B. Find the value of x. take 3x from both sides take 21 from both sides expand the brackets divide both sides by 4 AB simplify

Example 11 Solve add 5 to both sides multiply both sides by 3

Example 12 Solve multiply both sides by 7 take 4 from both sides

Example 13 Solve multiply both sides by 5 add 3 to both sides divide both sides by 2

Example 14 Solve take 3 from both sides multiply both sides by x divide both sides by 4

Example 15 Solve multiply both sides by (x + 2) expand the brackets take 12 from both sides divide both sides by 6

Example 15 Solve multiply both sides by 15 expand the brackets take 3x from both sides add 30 to both sides 5 3 divide both sides by 2

There is a quicker method for doing the last example. The quick method can be used when there is a ‘single’ fraction on each side of the ‘=‘ sign. ‘cross multiply’ expand the brackets take 3x from both sides add 30 to both sides divide both sides by 2

Example 16 Solve ‘cross multiply’ expand the brackets add 5x to both sides take 4 from both sides divide both sides by 9

Example 17 Solve ‘cross multiply’ expand the brackets take 8x from both sides add 9 to both sides