Algebra: Equations
Solving equations is the algebra skill of finding the value of an unknown letter that makes both sides of an equation equal. Equations range from simple one-step equations like x + 7 = 15 to two-step equations, equations with brackets, and equations with the unknown on both sides. This topic also covers forming equations from worded problems, such as shape perimeters and consecutive numbers, then solving them.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify what operations have been done to the unknown, in the order they were applied.
- Undo these operations in reverse order, applying the same operation to both sides each time.
- If there are brackets, expand them first before collecting like terms.
- If the unknown appears on both sides, collect all the unknown terms on one side and all number terms on the other.
- Simplify each side fully, then perform the final inverse operation to find the value of the unknown.
- Check your answer by substituting it back into the original equation.
Worked example
Solve the equation 4(x - 3) = 2x + 10.
- Expand the bracket: 4x - 12 = 2x + 10.
- Subtract 2x from both sides to collect x terms: 2x - 12 = 10.
- Add 12 to both sides: 2x = 22.
- Divide both sides by 2: x = 11.
- Check: 4(11-3) = 4 x 8 = 32, and 2 x 11 + 10 = 32. Both sides match.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Solve the equation 7x - 5 = 3x + 23.
A rectangle has length (x + 8) cm and width x cm. The perimeter of the rectangle is 52 cm. (a) Write an equation in x for the perimeter. (b) Solve your equation to find x. (c) Hence find the length of the rectangle.
Three consecutive even numbers have a sum of 84. Let the smallest number be n. Form an equation in n, solve it, and state the three numbers.
Free printable worksheet
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