# linear equation: solving (8/3)x - 3 = (2/3)x + 15

#### crappiefisher26

##### New member
The instructions say to "solve for x and check your result". My book doesn't give a very good example though:

. . .(8/3)x - 3 = (2/3)x + 15

The above means "eight-thirds x and two-thirds x".

#### jonboy

##### Full Member
So we have: $$\displaystyle \L \;\frac{8}{3}x\,-\, 3\,=\,\frac{2}{3}x\,+\,15$$

Combine like terms and solve for x.

#### Denis

##### Senior Member
jonboy said:
So we have: $$\displaystyle \L \;\frac{8}{3}x\,-\, 3\,=\,\frac{2}{3}x\,+\,15$$

Combine like terms and solve for x.
Crappy, if you multiply each term of Jonboy's equation by 3, you get:
8x - 9 = 2x + 45 : do you understand that?

#### crappiefisher26

##### New member
The example states the following.

6-(1/2)x=(3/5)+x

We need to isolate the variable x. We first add (1/2)x to both sides and subtract (3/5) from both sides.

6-(3/5)=x+(1/2)X

(27/5)=(3/2)x

(2/3) times (27/5)=(2/3) times (3/2)x

(18/5)=x

#### Mrspi

##### Senior Member
crappiefisher26 said:
The instructions say to "solve for x and check your result". My book doesn't give a very good example though:

. . .(8/3)x - 3 = (2/3)x + 15

The above means "eight-thirds x and two-thirds x".

We need to isolate the variable. To eliminate the (2/3)x from the right side, subtract (2/3)x from both sides of the equation:

(8/3)x - 3 - (2/3)x = (2/3)x + 15 - (2/3)x

Combine like terms:

(6/3)x - 3 = 15

Now, (6/3) is just 2, so we really have

2x - 3 = 15

Next, add 3 to both sides. This will get the variable term by itself on the left side:

2x - 3 + 3 = 15 + 3

Combine like terms again:

2x = 18

I think you can finish it.