# Solve for R (R+4)/6=5/6-(R-1)/4

R+46=56-R-14
Multiply both sides of the equation by 6.
R+4=(56-R-14)⋅(6)
Remove parentheses.
R+4=(56-R-14)⋅(6)
Simplify (56-R-14)⋅(6).
To write 56 as a fraction with a common denominator, multiply by 22.
R+4=(56⋅22-R-14)⋅6
To write -R-14 as a fraction with a common denominator, multiply by 33.
R+4=(56⋅22-R-14⋅33)⋅6
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply 56 and 22.
R+4=(5⋅26⋅2-R-14⋅33)⋅6
Multiply 6 by 2.
R+4=(5⋅212-R-14⋅33)⋅6
Multiply R-14 and 33.
R+4=(5⋅212-(R-1)⋅34⋅3)⋅6
Multiply 4 by 3.
R+4=(5⋅212-(R-1)⋅312)⋅6
R+4=(5⋅212-(R-1)⋅312)⋅6
Combine the numerators over the common denominator.
R+4=5⋅2-(R-1)⋅312⋅6
Simplify the numerator.
Multiply 5 by 2.
R+4=10-(R-1)⋅312⋅6
Apply the distributive property.
R+4=10+(-R–1)⋅312⋅6
Multiply -1 by -1.
R+4=10+(-R+1)⋅312⋅6
Apply the distributive property.
R+4=10-R⋅3+1⋅312⋅6
Multiply 3 by -1.
R+4=10-3R+1⋅312⋅6
Multiply 3 by 1.
R+4=10-3R+312⋅6
R+4=-3R+1312⋅6
R+4=-3R+1312⋅6
Simplify terms.
Cancel the common factor of 6.
Factor 6 out of 12.
R+4=-3R+136(2)⋅6
Cancel the common factor.
R+4=-3R+136⋅2⋅6
Rewrite the expression.
R+4=-3R+132
R+4=-3R+132
Factor -1 out of -3R.
R+4=-(3R)+132
Rewrite 13 as -1(-13).
R+4=-(3R)-1(-13)2
Factor -1 out of -(3R)-1(-13).
R+4=-(3R-13)2
Simplify the expression.
Rewrite -(3R-13) as -1(3R-13).
R+4=-1(3R-13)2
Move the negative in front of the fraction.
R+4=-3R-132
R+4=-3R-132
R+4=-3R-132
R+4=-3R-132
Move all terms containing R to the left side of the equation.
Add 3R-132 to both sides of the equation.
R+4+3R-132=0
To write R as a fraction with a common denominator, multiply by 22.
R⋅22+3R-132+4=0
Combine R and 22.
R⋅22+3R-132+4=0
Combine the numerators over the common denominator.
R⋅2+3R-132+4=0
Reorder R and 2.
2⋅R+3R-132+4=0
5⋅R-132+4=0
5⋅R-132+4=0
To write 4 as a fraction with a common denominator, multiply by 22.
5R-132+4⋅22=0
Combine 4 and 22.
5R-132+4⋅22=0
Combine the numerators over the common denominator.
5R-13+4⋅22=0
Simplify the numerator.
Multiply 4 by 2.
5R-13+82=0
5R-52=0
Factor 5 out of 5R-5.
Factor 5 out of 5R.
5(R)-52=0
Factor 5 out of -5.
5(R)+5(-1)2=0
Factor 5 out of 5(R)+5(-1).
5(R-1)2=0
5(R-1)2=0
5(R-1)2=0
5(R-1)2=0
Multiply both sides of the equation by 25.
25⋅5(R-1)2=25⋅0
Simplify both sides of the equation.
Simplify 25⋅5(R-1)2.
Cancel the common factor of 2.
Cancel the common factor.
25⋅5(R-1)2=25⋅0
Rewrite the expression.
15⋅(5(R-1))=25⋅0
15⋅(5(R-1))=25⋅0
Cancel the common factor of 5.
Cancel the common factor.
15⋅(5(R-1))=25⋅0
Rewrite the expression.
R-1=25⋅0
R-1=25⋅0
R-1=25⋅0
Multiply 25 by 0.
R-1=0
R-1=0
Add 1 to both sides of the equation.
R=1
Solve for R (R+4)/6=5/6-(R-1)/4

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