# Equations Worksheets – New & Engaging

### What Are Linear Equations?

Students learn how to solve equations from year 7 onward. Solving equations ranges in difficulty. Students may understand how to manipulate algebraic expressions before they are ready to solve equations.

### Linear Equations Example 1

The image below shows different examples of linear equations.

2c = 4 is different to x - 5 = -1. With the equation 2c = 4 we divide both sides by 2. The answer is c = 2. With x - 5 = -1 we add (-5) to both sides. The answer is x = 4 because -1 + (-5) equals 4. ### Linear Equations Example 2

The linear equation examples below are more tricky.

To solve the equation 2a + 2 - 4a = - 6, we first collect like terms. 2a - 4a is -2a. The equation becomes 2 - 2a = - 6. Next we subtract 2 from both sides. The equation becomes - 2a = - 8. Next we divide both sides by negative 2. We are left with an answer of a = 4. ### Linear Equations Example 3

The equations below involve division and or fractions. In the case of 4v / 5 = 8 we first multiply both sides by 5. Next we divide both sides by 4. The final answer is v = 10. We can always substitute the final answer into the original equation to see if it is correct. ### How do You Calculate An Equation?

Equations is a GCSE Foundation and GCSE Higher topic. Experienced teachers will have their own unique approach when teaching how to solve equations. We recommend the balancing method as this is a common way to introduce the topic solving equations. As prerequisite topics we suggest: simplifying expressions, or substituting into expressions.

### Balancing Method vs Function Machine Method

The image below shows an example of the balancing method as well as the function machine method. The equation 8a - 5 = 11 has been solved using the balancing method and the function machine method. a is the subject of the equation.

The final answer is a = 2. In the example below the equation 10 + 6y = 34 has been solved using the balancing method and the function machine method. y is the subject of the equation.

The final answer is y = 4. In the example below the equation x/12 - 5 =4 has been solved using the balancing method and the function machine method. x is the subject of the equation.

The final answer is x = 108. ## Equations Worksheets – New & Engaging

For Simultaneous Equations Cazoomy Worksheets try: Simultaneous Equations Worksheets. For Completing The Square Cazoomy Worksheets try: Completing The Square Worksheets. For Quadratic Equations Cazoomy Worksheets try: Quadratic Equations Worksheets.