大象传媒

Solving equations with 饾挋 on both sides

Part of MathsEquations

Key points

A visualisation of an equation as a set of scales. On the left side of the balance is a large block labelled x. On the right side of the balance, four small blocks, each labelled one. Written above: x equals four.
An equation is like a set of scales that are in balance.
  • An is like a set of scales that are in balance. The on either side of the equals sign (=) have the same value as each other.
  • Equations need to stay in balance. Do the same thing to both sides to keep the equation balanced, for example adding or subtracting the same amount from each side.
  • When a is it is often given a value of \(x\), although it is important to remember that any letter can be used to represent an unknown value.
  • The unknown variable (often the letter \(x\)) can take any value, including decimal and negative values.
A visualisation of an equation as a set of scales. On the left side of the balance is a large block labelled x. On the right side of the balance, four small blocks, each labelled one. Written above: x equals four.
An equation is like a set of scales that are in balance.
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Solving equations when both unknown terms are positive

  • If both unknown variables are positive, the first step is to subtract one of these \(x\) terms.
  • Subtracting the \(x\) term which has the smaller means that negative terms can be avoided.
  • The \(x\) term with the smallest coefficient can appear on the left or the right of the = sign.
  • This will reduce the number of terms and lead to a new (still balanced) with just one variable.
  • Check the solution by substituting the final answer back into the original equation.

Example

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  1. A visualisation of an equation as a set of scales. On the left side of the balance are three large blocks, each labelled x and four small blocks, each labelled one. On the right side of the balance, one large block labelled x and twelve small blocks, each labelled one. Written above: three x plus four equals x plus twelve.

    The equation 3饾挋 + 4 = 饾挋 + 12 can be represented by the diagram above. The equals sign between the two sets of terms shows that the equation is in balance.

Question

Find the value of the unknown term \(x\) when 2\(x\) + 5 = \(x\) + 8

A visualisation of an equation as a set of scales. On the left side of the balance are two large blocks, each labelled x and five small blocks, each labelled one. On the right side of the balance, one large block labelled x and eight small blocks, each labelled one. Written above: two x plus five equals x plus eight.

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Solving equations when one unknown term is negative

  • If one unknown is negative, the first step is to add one of the \(x\) .
  • Adding an \(x\) term helps avoid unknown values with negative .
  • The \(x\) term with a negative coefficient can appear on the left or the right of the equals sign.
  • This will reduce the number of terms and lead to a new equation that is still in balance, with just one unknown variable.

Example

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  1. A visualisation of an equation using algebra tiles. On the left are nine tiles labelled one, and two negative x tiles. On the right is one positive x tile and three tiles labelled one. Between the images on the left and right is an equals sign. Written above: nine subtract two x equals x plus three.

    The equation 9 - 2饾挋 = 饾挋 + 3 can be represented by the diagram above. The equals sign between the two sets of terms shows that the equation is in balance.

Question

Find the value of the unknown term \(x\) when \(x\) + 5 = 17 鈥 3\(x\)

A visualisation of an equation using algebra tiles. On the left is one positive x tile and five tiles labelled one. On the right is one tile labelled seventeen and three negative tiles. Between the images on the left and right is an equals sign. Written above: x plus five equals seventeen subtract three x.

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Practise solving equations with 饾挋 on both sides

Quiz

Practise solving equations with \(x\) on both sides with this quiz. You may need a pen and paper to help you with your answers.

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Game - Divided Islands

Using your maths skills, help to build bridges and bring light back to the islands in this free game from 大象传媒 Bitesize.

Play the Divided Islands game!
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More on Equations

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