Question

How do you solve for x in `2x+9= 7x-1`?

Answer 1

`color(green)(x=2)`

With practice you will be able to cut out a lot of the steps I have shown you!

Explanation:

`color(blue)("Method")`

manipulate so that you have all the x's and their coefficients on one side of the = and all the numbers on the other

Manipulate the x's so that you end up with just a single x and everything else on the other side of the =

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`color(blue)("Solving your question")`

Given:`" "color(brown)(2x+9=7x-1)`

Keep `7x` where it is but move the `2x` as `7x-2x` is positive

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

`" "color(brown)(2x+9color(blue)(-2x)=7x-1color(blue)(-2x))`

`" "color(brown)(0+9=7x-2x-1`

`" "color(brown)(9=5x-1`

Add `color(blue)(1)` to both sides

`" "color(brown)(9color(blue)(+1)=5x-1color(blue)(+1)`

`" "color(brown)(10=5x+0)`

Write as: `color(brown)(5x=10)" "` ( this is done to match convention)

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

`" "color(brown)( (5x)/(color(blue)(5)) =10/(color(blue)(5))`

`" "color(brown)( 5/5 x =2`

But `5/5=1` giving

`color(green)(x=2)`