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
Solve `6x-7=4x-3`.
| `6x` | `-` | `7` | `=` | `4x` | `-` | `3` | |
| Subtract `4x` from both sides | `2x` | `-` | `7` | `=` | `` | `-` | `3` |
| Add 7 to both sides | `2x` | `` | `` | `=` | `` | `` | `4` |
| Divide both sides by 2 | `x` | `` | `` | `=` | `` | `` | `2` |
Check `6(2)-7=4(2)-3` ✔
Answer: `x=5`
Solve `7x+5=4x-4`.
| `7x` | `+` | `5` | `=` | `4x` | `-` | `4` | |
| Subtract `4x` from both sides | `3x` | `+` | `5` | `=` | `-` | `4` | |
| Subtract 5 from both sides | `3x` | `=` | `-` | `9` | |||
| Divide both sides by 3 | `x` | `=` | `-` | `3` |
Check `7(-3)+5=4(-3)-3` ✔
Answer: `x=-3`