Solving Equations Worksheet

Solving equations at a glance

Solving equations involves rearranging equations to make the unknown the subject in order to work out the solution. To rearrange an equation we use the inverse operation.

There are a variety of different types of equations to solve. The simplest equations are linear one-step equations, two step equations and multi-step equations. Equations can involve fractions and require the use of order of operations to correctly find the unknown variable. Linear equations can also involve brackets which can expanded and they may include an unknown variable on both sides of the equations. Equations involving a square root or indices may be solved in a similar way, by rearranging to make the unknown the subject.

Solving equations also requires solving quadratic equations. Quadratic equations often have two different solutions and can be solved using several different methods. One method involves setting the quadratic expression equal to zero and factorising it into brackets. The solutions can be found by considering each factor being equal to zero. Another method is to solve quadratic equations using the quadratic formula where the coefficients of the different terms are substituted into the quadratic formula. The solutions can be written as surds or decimals. The final method is completing the square which requires careful algebraic manipulation to rearrange the quadratic equations to give two solutions. The solutions are often given in surd form.

 Looking forward, students can progress with more solving equations worksheets and to additional algebra worksheets, for example a simplifying expressions worksheet or straight line graphs worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.