# Linear Equation: (5/3x)-(5/2)=-(4/9)

#### crappiefisher26

##### New member
Ok heres the question. (5/3x)-(5/2)=-(4/9)

Here is how i understand how to figure it out. It asks me to solve for x, write answer as fraction and in simpilest form.

6(5/3x-5/2)=6(-4/9)

then i got
6(5/3x)-6(-5/2)=6(-4)

30x-30=-24

30x-30+30=-24

30x=-24

Then i divided both sides by 30 and got -(4/5) but that wasnt right.

heres another question that i asked my professor about. same type.

(9/8x)+(3/4)=(7/2)

8((9/8x)+(3/4))=8(7/2)

8(9/8x)+8(3/4)=8(7/2)

9x+2(3)=4(7) simplifies to 9x+6=28

then he got 9x+6-6=28-6

9x=22, then he divided both sides by 9 and got (22/9).

Im really confused. cause i did a couple and emailed him all my work and answers and they were wrong. So i dont know what to do anymore.

#### royhaas

##### Full Member
Re: Linear Equation

crappiefisher26 said:
Ok heres the question. (5/3x)-(5/2)=-(4/9)

Here is how i understand how to figure it out. It asks me to solve for x, write answer as fraction and in simpilest form.

6(5/3x-5/2)=6(-4/9)

then i got
6(5/3x)-6(-5/2)=6(-4)
Your next step should read $$\displaystyle 10x +15 = -8/3$$.

#### stapel

##### Super Moderator
Staff member
crappiefisher26 said:
(5/3x)-(5/2)=-(4/9)

6(5/3x-5/2)=6(-4/9)

6(5/3x)-6(-5/2)=6(-4)

30x-30=-24
What you posted would seem to indicate the following:

. . . . .$$\displaystyle \L \frac{5}{3x}\,-\,\frac{5}{2}\,=\,-\frac{4}{9}$$

But going from the third line (in the quote above) to the fourth seems to indicate that you meant the following:

. . . . .$$\displaystyle \L \frac{5}{3}\,x\,-\,\frac{5}{2}\,=\,-\frac{4}{9}$$

Is this latter guess correct? That is, did you mean "(5/3)x - 5/2 = -4/9"? Also, the only way the 6 could have multiplied (on the right-hand side) to give a "-4" would be if that fraction were a "-4/6" rather than "-4/9". Please confirm or correct.

Thank you.

Eliz.

#### crappiefisher26

##### New member
this is correct. But im all confused now on how to do it from start to finish.
Could ya write it out and reply back to me.
Thanks.

#### jonboy

##### Full Member
Given: $$\displaystyle \L \;\frac{5}{3}\,x\,-\,\frac{5}{2}\,=\,-\frac{4}{9}$$

Add $$\displaystyle \L \,\frac{5}{2}$$: $$\displaystyle \;\L \frac{5}{3}\,x\,=\,\frac{37}{18}$$

Divide by $$\displaystyle \L \,\frac{5}{3}$$: $$\displaystyle \L \;x\,=\,\frac{37}{30$$