# solving linear equations: 5(3x - 1) - 6x = 3x - 2

#### crappiefisher26

##### New member
Solving linear equations with several occurences of the variable.

Heres the questions

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

2) 5(8-x)=3x

3) 5x=3(x-6)

thought i had it but i was wrong.

#### jonboy

##### Full Member
Hello Fisher!

1) $$\displaystyle \L 5(3x-1)-6x=3x-2$$

Distributive Property (5): $$\displaystyle \L \;15x-5-6x=3x-2$$

Simpilication: $$\displaystyle \L \;9x-5=3x-2$$

Subtraction Property (3x): $$\displaystyle \L \;6x-5=-2$$

Addition Property (5): $$\displaystyle \L \;6x=3$$

Division Property (6): $$\displaystyle \L \;x=\frac{1}{2}$$

2) $$\displaystyle \L 5(8-x)=3x$$

Distributive Property: $$\displaystyle \L \;40-5x=3x$$

Addition Property: $$\displaystyle \L \;40=8x$$

Division Property (8): $$\displaystyle \L \;x=5$$

3)$$\displaystyle \L \;5x=3(x-6)$$

Distributive Property (3): $$\displaystyle \L \;5x=3x-18$$

Subtraction Property (3x): $$\displaystyle \L 2x=-18$$

Division Property: $$\displaystyle \L \;x= - 9$$

#### crappiefisher26

##### New member
Thanks. One more quick question.

same problem.

4) 4(3x+5)=18x

5) 4(x+3)=12x-2

6) 5x+2(3x-4)=14x+7

These are some tricky problems eh?

#### jonboy

##### Full Member
I gave you a few now it is your turn to attempt these and show me what you get. Check your answer by plugging back your variable in and making sure the equation is balanced. Use what I have shown you to solve these and post what you think is correct and we will check your work.

#### stapel

##### Super Moderator
Staff member
crappiefisher26 said:
These are some tricky problems eh?
Not really; they're fairly straight-forward. And you've already had half of the posted exercises completed for you. Now it's your turn to show some effort.

Please attempt these exercises. If you get stuck, please reply clearly showing (line by line) what you have tried and how far you have gotten.

Thank you.

Eliz.

#### crappiefisher26

##### New member
Just checkin to see if i did this right.

4(x+3)=12x-2

4x+12=12x-2

subtracted 12x on each side

-8x+12=-2

subtracted 12 on each side

-8x=-14

divided by -8x on each side

got x=1.75 or 1 3/4. Is that correct? I believe so.

#### crappiefisher26

##### New member
Whats the Deal

4(3x+5)=18x

got 12x+20=18x

subtracted 12x on each side

20=6x

divided by 6x on each side and got 3.33 repeating. would the answer just be 20/6?

#### jonboy

##### Full Member
crappiefisher26 said:
Just checkin to see if i did this right.

4(x+3)=12x-2

4x+12=12x-2

subtracted 12x on each side

-8x+12=-2

subtracted 12 on each side

-8x=-14

divided by -8x on each side

got x=1.75 or 1 3/4. Is that correct? I believe so.
Fill it back in to see: $$\displaystyle \;-8(1\frac{3}{4})+12= -2\, \to\, -14+12=-2\,\to\, -2= -2$$

So yes that is correct. Do this w/your other problems as well to make sure you do not make a simple mistake.

#### jonboy

##### Full Member
Re: Whats the Deal

crappiefisher26 said:
4(3x+5)=18x

got 12x+20=18x

subtracted 12x on each side

20=6x

divided by 6x on each side and got 3.33 repeating. would the answer just be 20/6?
You do not have it in simpiest form. You should find the LCM (which in this case is 2).

Hence: $$\displaystyle \frac{20}{6}\, \to\, \frac{10}{3}$$