Question

How do you solve `10=-2/3(4x+5)`?

Answer 1

`x=-5`

Working out shown in a lot of detail!

Explanation:

Given:`" " 10=color(brown)(color(blue)(-2/3)(4x+5))`

Multiply out the brackets giving:

`" "10= color(brown)({color(blue)((-2/3))xx4x }" "+" "{color(blue)((-2/3))xx5})`

The 'squiggly' brackets (braces) are only there to group parts to make understanding easier. They serve no other purpose

`10=-8/3 x- 10/3`

Add `color(blue)(10/3)` to both sides

`color(brown)(10color(blue)(+10/3)=-8/3 x -10/3color(blue)(+10/3))`

`40/3=-8/3 x+0`

`40/3=-8/3 x`

Multiply both sides by`color(blue)( 3)`

`40/(cancel(3)) xx cancel(color(blue)(3)) = -8/(cancel(3)) x xxcancel(color(blue)(3))`

Divide both sides by 8, divide by 8 is the same as `xx1/8`

`40/8= -8/8 x`

So `" "-x=5" "` Notice the `x` is negative

Multiply both sides by (-1) giving

`x=-5`