Question

Which of the following is a solution to the equation ¾x-12=-18?

4.5
-22.5
-40
-8

Answer 1

`\frak{Hi!}`

`\orange\hspace{300pt}\above2`

We have the equation
`\large\boldsymbol{\sf{\displaystyle(3)/(4)x-12=-18}}`.

First we should add 12 to both sides of the equation.

`\large\boldsymbol{\sf{\displaystyle(3)/(4)x=-18+12}}`. Simplify

`\large\boldsymbol{\sf{\displaystyle(3)/(4)x=-6}}`.

This done, let's multiply the equation by 4. You'll see why

`\large\boldsymbol{\sf{\displaystyle(3)/(\\ot4)x*\\ot4=-6*4}}`

Did you see how on the left, the 4's cancelled? That's

because dividing by 4 and then multiplying the same

number, or the result, by 4, are operations that undo each

other.

This being said, let's finish solving this equation in terms of x

`\large\boldsymbol{\sf{3x=-24}}`. See how this works?

Now, remember that we ought to use inverse operations

to solve for x. These are operations that undo each other.

So if x is multiplied by 3, we should... divide by 3!

Also, please keep in mind that we can only divide the left side

by 3 if we divide the right side by 3.

`\large\boldsymbol{\sf{\displaystyle(3x)/(3)=\displaystyle(-24)/(3)}}`. Once again the 3s on the left cancel, leaving

x. Wait! Isn't that what we wanted? Yepp, sure!

The right side is now -8. Thus,

`\large\boldsymbol{\sf{x=-8}}`

`\orange\hspace{300pt}\above3`