Equations with Unknowns on Both Sides (WJEC GCSE Maths & Numeracy (Double Award): Foundation): Revision Note

Unknown on both sides

How do I solve linear equations with x terms on both sides?

• If a linear equation contains the unknown variable on both sides, collect the x terms together on one side 

  • To do this, choose a side you wish to remove the x  term from

    •  this should be the side with the lowest value x  term

  • Apply the opposite of that term to both sides

• For example, solve  $4x-7=11+x$

• Let's remove the x  term on the right-hand side

• x  has been added, so subtract x  from both sides 

$\begin{array}{rcl}4x-7& =& 11+x\end{array}$

$\begin{array}{rcl}& & \left(-x\right)\left(-x\right)\end{array}$

$\begin{array}{rcl}3x-7& =& 11\end{array}$

• There are no longer any x  terms on the right

• The 4x  has become 3x  on the left

• This now has the same form as equations with one variable

  • Solve it by adding 7 then dividing by 3         

$\begin{array}{rcl}3x-7& =& 11\\ 3x& =& 18\\ x& =& 6\end{array}$