# Solving Linear Equation

#### crappiefisher26

##### New member
I dont want the answer just want someone to walk through one of these with me.

7(3x+11)=9(3-6x)

and

5(2x-1)-3(x-4)=4(x+4)

Thanks.

#### jonboy

##### Full Member
We are going to have to use Distributive Property:

$$\displaystyle \L 7(3x+11)=7\times3x \;&\; 7\times11\,\to\,21x+77$$

$$\displaystyle \L 9(3-6x)=9\times3\;&\;9\times-6x\,\to\,27-54x$$

Hence: $$\displaystyle \L \;21x+77=27-54x$$

The other works the same way just more distribution. BTW the Distribution Propery and Distributive Propery are the same thing.

#### Denis

##### Senior Member
HEY, nice and clear Jonboy

3(x + 2) = 3x + 6
I've always wondered why THE GURUS named such a simple multiplication
"The Distributive Property" :evil:
Such a name is enough to create terror in a poor innocent student :wink:

#### tkhunny

##### Moderator
Staff member
Isn't the REAL name the "Distributive Property of Multiplication Over Addition"?

#### Denis

##### Senior Member
Tyler: grandpa, how do I solve 3(x + 2) = 18? Isn't that simply 3x + 6 = 18?

Denis: yes, correct.

Tyler: but but...it can't be that simple; the teacher told us to use "the Distributive Property of Multiplication Over Addition"

#### jonboy

##### Full Member
LOL Denis. If they called it that I would definetly be confused.

#### crappiefisher26

##### New member
Still cant figure them out. Help please.
Thanks

#### Denis

##### Senior Member
$$\displaystyle \L \;21x+77=27-54x$$

Are you saying you can't solve that for x?

#### crappiefisher26

##### New member
Heres what i got its not right!!

21x+77=27-54x

subtract 21 x from each side

77=27-75x

subtract 27 from each side

50=-77x

divide by -77

#### stapel

##### Super Moderator
Staff member
Hint: 54 + 21 = 75, not 77.

Eliz.

#### crappiefisher26

##### New member
How bout the first one. I cant figure it out.

#### crappiefisher26

##### New member
ok. heres the equation again.

7(3x+11)=9(3-6x)

21x+77=27-54x

subtract 21 x from both sides

77=27-33x

subtract 27

50=-33x

divide by -33

x=1.51 repeating. that doesnt work if ya plug it back into the original equation.

#### stapel

##### Super Moderator
Staff member
Hint: 54 + 21 does not equal 33.

Eliz.

#### crappiefisher26

##### New member
7(3x+11)=9(3-6x)

21x+77=27-54x

subtract 21 from each side

77=27-75x

subtract 27 from each side

50=-75x

divide by -75

x=.6666666667

thats not correct. okay somebody walk through this with me, cause i cant get the right answer.

#### stapel

##### Super Moderator
Staff member
Hint: The result of dividing a positive by a negative is not a positive.

Suggestion: Don't use decimal approximations; stick to the exact fractions.

Eliz.

#### crappiefisher26

##### New member
ok the fraction for -.6666666667 would be -(3/4) but i tried that in the original equation and it wasnt right. so could ya walk through the steps with me. Thanks.

#### stapel

##### Super Moderator
Staff member
No, 0.66666666... is not the decimal approximation for 3/4 = 0.75.

Try reducing 50/75 by dividing out the 25.

Eliz.

#### Denis

##### Senior Member
crappiefisher26 said:
7(3x+11)=9(3-6x)
21x+77=27-54x
subtract 21 from each side
77=27-75x
subtract 27 from each side
50=-75x
divide by -75
x=.6666666667
thats not correct. okay somebody walk through this with me, cause i cant get the right answer.
Boy, crappy, you sure seem to enjoy complicating your life!

You're correct to here:
-75x = 50
now dividing by -75 gives:
-75x/-75 = 50/-75
x = -(50/75)
x = - 2/3 : THAT'S IT; STOP!; Stapel told you to STAY with fractions :twisted: