Question

How do you solve `7x – 7 = 2x + 8`?

Answer 1

`x = 3`

Explanation:

This is solved by simply moving the terms with `x` to the same side and the integers to the same side. You can do this by subtracting `2x` from both sides and adding `7` to both sides. This gives:

`5x = 15`

Then divide both sides by `5`, which gives `x = 3`.

Answer 2

`x=3`

Explanation:

The one rule you must follow is that what you do to one side of the equation you do to the other. Otherwise the 'equals' sign becomes false

Example: `7=7` this is true as the value on both sides is the same.

If I apply `7-2=7` this becomes false as we have 5=7 which is not true. How ever

`7-2=7-2` is true. We have applied the action to both sides.
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This is why what I wrote is important:

Given:`" "color(brown)(7x-7=2x+8)`

Subtract `color(blue)(2x)` from both sides

`" "color(brown)(7xcolor(blue)(-2x)-7=2xcolor(blue)(-2x)+8)`

But `2x-2x =0`

`" "5x-7=0+8`

Add `color(blue)(7)` to both sides

`" "color(brown)(5x-7color(blue)(+7)=8color(blue)(+7)`

But `-7 +7 = 0`

`" "5x+0=15`

Divide both sides by `color(blue)(5)`

`" "color(brown)(5/(color(blue)(5)) x=15/(color(blue)(5)))`

But `5/5=1" and "15/5= 3`

`" "color(magenta)(x=3)`

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