# need help solving (X - 5)/6 = (X + 4)/2

#### misschristine_b

##### New member
I'm cannot seem to understand how to do this problem, can anyone explain it to me?

(X - 5) / 6 = (X + 4) / 2

#### jwpaine

##### Full Member
Re: NEED HELP

misschristine_b said:
I'm cannot seem to understand how to do this problem, can anyone explain it to me?

X - 5 X + 4
----- = -------
6 2[/list]
$$\displaystyle \L \frac{x - 5}{6} = \frac{x + 4}{2}$$

Cross multiply:

$$\displaystyle \L 2(x - 5) = 6(x + 4)$$

Solve for x..
John

#### misschristine_b

##### New member
Thank you so much, we haven't got to that part in our class but it's part of our homework.

#### soroban

##### Elite Member
Re: NEED HELP

Hello, Christine!

$$\displaystyle \L\frac{x\,-\,5}{6} \:=\:\frac{x\,+\,4}{2}$$

Maybe you didn't know about cross-multiplying,
. . but you do know how to do this . . .

Multiply both sides by 6: $$\displaystyle \L\:6\.\cdot\frac{x\,-\,5}{6}\;=\;6\,\cdot\,\frac{x\,+\,4}{2}$$

. . and we get: $$\displaystyle \L\:x\,-\,5 \;= \;3(x\,+\,4)$$

I trust you can finish it now . . .

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Here's another approach (not usually recommended) . . .

We have: $$\displaystyle \L\:\frac{x\,-\,5}{6}\;=\;\frac{x\,+\,4}{2}$$

Then: $$\displaystyle \L\:\frac{x}{6}\,-\,\frac{5}{6}\;=\;\frac{x}{2}\,+\,\frac{4}{2}$$

Subtract $$\displaystyle \frac{x}{2}$$ from both sides: $$\displaystyle \L\;\frac{x}{6}\,-\,\frac{x}{2}\,-\,\frac{5}{6}\;=\;2$$
. . and we have: $$\displaystyle \L\:-\frac{x}{3}\,-\,\frac{5}{6}\;=\;2$$

Add $$\displaystyle \frac{5}{6}$$ to both sides: $$\displaystyle \L\;-\frac{x}{3}\;=\;2\,+\,\frac{5}{6}$$
. . and we have: $$\displaystyle \L\:-\frac{x}{3}\;=\;\frac{17}{6}$$

Multiply both sides by -$$\displaystyle 3:\;\;\L-3\left(-\frac{x}{3}\right) \;=\;-3\left(\frac{17}{6}\right)$$

. . Therefore: $$\displaystyle \L\:x\;=\;-\frac{17}{2}$$