Solving Equations Unknown on Both Sides

Solving Equations Unknown on Both Sides

GCSE(F), GCSE(H),

Where an unknown appears on both side of an equation, the equation needs to be re-arranged so that all the values of the unknown are on one side of the equation, and the numbers on the other:

Start by identifying on which side of the equation the lowest value of the unknown appears

Remove the lowest unknown value from both sides of the equation

The equation then can be solved as an equation with an unknown on one side

Examples

1. Solve `6x-7=4x-3`.

Answer: `x=5`

`6x-7=4x-3` (first subtract 4x from both sides)

`2x-7=-3` (next add 7 to both sides)

`2x=4` (finally divide both sides by 2)

`x=2`

2. Solve `7x+5=4x-4`.

Answer: `x=-3`

`7x+5=4x-4` (first subtract 4x from both sides)

`3x+5=-4` (next, subtract 5 from both sides)

`3x=-9` (finally, divide both sides by 3)

`x=-3`

Check the answer: `7(-3)+5=4(-3)-4`, which is true.