Question

How do you solve `2x/3+9=-7`?

Answer 1

Use the formula PESADM
`x = -24`

Explanation:

In solving for an unknown always work backwards.
First remove any Parenthesis and Exponents

`x/3` is actually a parenthesis `(x/3)`

To remove the parenthesis multiply everything by 3. This gives

`cancel3 xx 2(x/cancel3) + 3 xx 9 = 3 xx -7` The result is

`2x + 27 = - 21`

Now that the PE is taken care of do SA (subtraction and addition)

Subtract 27 or add - 27 to both sides This gives

`2x + 27 - 27 = -21 -27" "` The result is

(subtracting from a negative gives more negatives)
A negative goes down, adding another negative goes further down. So the answer is very down
Think " I fell into a burning ring of fire I went down down down and the flame went higher and it burns burns burns the ring of fire".

`2x = - 48`

The PE and the SA are taken care of now do the DM

Divide both sides by `2" "` This gives

`(2x)/2 = -48/2 " "` The result is

`x = -24` ( a negative divided by a positive is a negative)

PESADM Think if you find you lost your cell phone in PE you are a SAD M(am)

Answer 2

It is not clear what is intended in the first term? `2 x/3`
There are two possible solutions.
`x = -54 " or " x = -24`

Explanation:

It is not clear what is intended in the first term? `2 x/3`

Is this to be regarded as a mixed fraction, which is generally not used in algebra?

There is nothing to indicate that is is a multiplication?

One of `" "2(x/3) " "2*x/3 " " 2xx x/3` would have been clearer

Let's look at both possibilities.

Option 1

Write `2 x/3` as an improper fraction, giving `(6+x)/3`

`(6+x)/3 +9color(red)(-9) = -7color(red)(-9)" "larr` add -9 to both sides

`(color(blue)(3xx)(6+x))/3 = -16color(blue)(xx3)color(white)(xxxxxxxxx)larr xx 3` on both sides

`6+x = -48" "larr` subtract 6 from both sides

`x = -48-6`

`x = -54`

Option 2

`2(x/3) +9color(red)(-9) = -7color(red)(-9)" "larr` subtract 9 from each side

`(color(blue)(3xx)2x)/3 = -16color(blue)(xx3)color(white)(xxxxxxxxx)larr xx 3` on both sides

`2x = -48`

`x = -24`