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

Oct 4, 2016

$x = - 24$

Explanation:

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

$\frac{x}{3}$ is actually a parenthesis $\left(\frac{x}{3}\right)$

To remove the parenthesis multiply everything by 3. This gives

$\cancel{3} \times 2 \left(\frac{x}{\cancel{3}}\right) + 3 \times 9 = 3 \times - 7$ The result is

$2 x + 27 = - 21$

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

Subtract 27 or add - 27 to both sides This gives

$2 x + 27 - 27 = - 21 - 27 \text{ }$ 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".

$2 x = - 48$

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

Divide both sides by $2 \text{ }$ This gives

$\frac{2 x}{2} = - \frac{48}{2} \text{ }$ 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)

Oct 19, 2016

It is not clear what is intended in the first term? $2 \frac{x}{3}$
There are two possible solutions.
$x = - 54 \text{ or } x = - 24$

Explanation:

It is not clear what is intended in the first term? $2 \frac{x}{3}$

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 $\text{ "2(x/3) " "2*x/3 " } 2 \times \frac{x}{3}$ would have been clearer

Let's look at both possibilities.

Option 1

Write $2 \frac{x}{3}$ as an improper fraction, giving $\frac{6 + x}{3}$

$\frac{6 + x}{3} + 9 \textcolor{red}{- 9} = - 7 \textcolor{red}{- 9} \text{ } \leftarrow$ add -9 to both sides

$\frac{\textcolor{b l u e}{3 \times} \left(6 + x\right)}{3} = - 16 \textcolor{b l u e}{\times 3} \textcolor{w h i t e}{\times \times \times \times x} \leftarrow \times 3$ on both sides

$6 + x = - 48 \text{ } \leftarrow$ subtract 6 from both sides

$x = - 48 - 6$

$x = - 54$

Option 2

$2 \left(\frac{x}{3}\right) + 9 \textcolor{red}{- 9} = - 7 \textcolor{red}{- 9} \text{ } \leftarrow$ subtract 9 from each side

$\frac{\textcolor{b l u e}{3 \times} 2 x}{3} = - 16 \textcolor{b l u e}{\times 3} \textcolor{w h i t e}{\times \times \times \times x} \leftarrow \times 3$ on both sides

$2 x = - 48$

$x = - 24$