Question

How do you solve `2( x - 5) - x = 4x - 7`?

Answer 1

Solution method given in a lot of detail.

`x=-1`

Explanation:

Using first principles.

Note that the shortcut method is a lot faster!

Multiply everything inside the brackets by (+2) giving:

`2x-10-x=4x-7`

Changing the order:

`2x-x-10=4x-7`

`x-10=4x-7`

Subtract `color(red)(x)` from both sides

`color(green)(xcolor(red)(-x)-10" "=" "4xcolor(red)(-x)-7)`

But `x-x=0`

`0-10" "=" "3x-7`

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

`color(green)(-10color(red)(+7)" "=" "3x-7color(red)(+7))`

But -7+7=0#

`-3" "=" "3x+0`

Divide both sides by 3

But `3/3=1 and (-3)/3=-1`

`x=-1`

Answer 2

`x=-1`

Explanation:

The first step is to distribute the bracket and simplify the left side of the equation.

`2x-10-x=4x-7`

`rArrx-10=4x-7`

subtract 4x from both sides.

`x-4x-10=cancel(4x)cancel(-4x)-7`

`rArr-3x-10=-7`

add 10 to both sides.

`-3xcancel(-10)cancel(+10)=-7+10`

`rArr-3x=3`

divide both sides by - 3

`(cancel(-3) x)/cancel(-3)=3/(-3)`

`rArrx=-1`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`"left side "=2(-1-5)-(-1)`

`color(white)(xxxxxx)=(2xx-6)+1`

`color(white)(xxxxxx)=-12+1=-11`

`"right side "=(4xx-1)-7=-4-7=-11`

`rArrx=-1" is the solution"`