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)

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

Add 10 and 3.

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

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

Add R⋅2 and 3R.

Reorder R and 2.

2⋅R+3R-132+4=0

Add 2⋅R and 3R.

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

Add -13 and 8.

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 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