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In this problem I'm solving an equation involving the variable x
And I am going to chose to do that
By the method where I clear the fractions
So that I'm working only with integers in the problem
In order to clear fractions I need to find the least common denominator
In this case the least common denominator of the fractions is 16
So I am going to multiply both sides of the equations by 16
The left side of the equation has several terms
So I will be distributing the 16 and multiplying each term by 16
So my next step with show that
So I can put the 16 over 1
So I can easily see what I will be cancelling
As I go ahead and multipy those
So I have distributed the 16. Each term is multiplied by 16
Now I can do some cross-cancelling to eliminate the denominators
So I will work on each little sub-problem
16 over 1 times seven-eighths
I can cancel a common factor of 8 in the top and the bottom
And end up with 14x plus 16 minus
Cancel the common factor of 16
11x equals
Common factor of 4 cancels out there
So I get equals 4
I have now gone from an equation that contained fractions
To an equivalent equation that only contains integers
As my coefficients and constants
My next step now will be to work on solving this equation
So I will simplify
The left hand side of the equaion
Since it has several terms that would be like terms
I could rearrange it if I like
14x minus 11x plus 16 equals 4
And I have these two like terms
14x minus 11x gives
3x plus 16 equals 4
At this point I can use my Addition Property of Equality
To eliminate the constant term to isolate the 3x, my variable term
So in order to do that I am going to subtract 16 from both sides of the equation
I'll get 3x equals negative 12
And finally I want to isolate the x
So I use my Multiplication Property of Equality
To eliminate that coefficient
To eliminate 3 here I will divide by 3
And I will have to do the same to the other side of the equation
And I'll end up with just one x equals
Excuse me, I kind of got down a little to low there, sorry
One x equals negative 4. And that will be my solution