Linear equations Linear equations are the easiest type of equation to solve because the unknown is not raised to any power other than 1. We can solve linear equations by rearrangement. We must do the same operation on both sides of the equals sign. For example: x – 19 = – 8 Add 19 to both sides: x = 11 7x = 42 Example 2: Divide both sides by 7: x = 6

Linear equations When more than one operation is performed on the unknown we need to solve the equation in several steps. For example, 4x + 5 = 29 subtract 5 from both sides: 4x = 24 divide both sides by 4: x = 6 Teacher notes Establish that for more complex equations a more rigorous method is required. Remind pupils that we are trying to get the unknown x on its own on the left hand side of the equals sign. Photo credit: © Mitar Vidakovic, Shutterstock.com Check that 4 × 6 + 5 is equal to 29 in the original equation.

Equations with unknowns on both sides In some cases the unknown appears on both sides of the equals sign. For example: 8x – 2 = 2x + 1 We need to work systematically to get the unknowns on the left and the numbers on the right. Remember to perform the same operations on both sides. unknowns numbers 8x – 2 = 2x + 1 Teacher notes Start by explaining that we only want terms containing x on the left-hand side. Ask pupils how we could ‘get rid of’ the – 2 from the left-hand side (by adding 2 to both sides of the equation). Next, ask how we could ‘get rid of’ the 2x from the right-hand side (by adding 2x to both sides of the equation). We could write 3 ÷ 6 as a fraction, 3/6. This then cancels to 1/2. It is usually better to write the solution as a vulgar fraction when the equivalent decimal cannot be written exactly. The solution should be substituted into the original equation to make sure the solution is correct. Photo credit: © Noam Armonn, Shutterstock.com add 2 to both sides: 8x = 2x + 3 subtract 2x from both sides: 6x = 3 divide both sides by 6: x = 0.5

Equation solving 3 Teacher notes This activity allows you to practice solving equations. Type 3 equations involve the unknown on both sides of the equation.

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