2d+14=1112

Subtract 14 from both sides of the equation.

2d=1112-14

To write -14 as a fraction with a common denominator, multiply by 33.

2d=1112-14⋅33

Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.

Multiply 14 and 33.

2d=1112-34⋅3

Multiply 4 by 3.

2d=1112-312

2d=1112-312

Combine the numerators over the common denominator.

2d=11-312

Subtract 3 from 11.

2d=812

Cancel the common factor of 8 and 12.

Factor 4 out of 8.

2d=4(2)12

Cancel the common factors.

Factor 4 out of 12.

2d=4⋅24⋅3

Cancel the common factor.

2d=4⋅24⋅3

Rewrite the expression.

2d=23

2d=23

2d=23

2d=23

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 3d. The 2d expression needs to be multiplied by 33 to make the denominator 3d. The 23 expression needs to be multiplied by dd to make the denominator 3d.

2d⋅33=23⋅dd

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3d.

2(3)

Multiply 2 by 3.

63d=23⋅dd

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 3d.

2(d)

Multiply 2 by d.

63d=2d3d

63d=2d3d

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

6=2d

Rewrite the equation as 2d=6.

2d=6

Divide each term in 2d=6 by 2.

2d2=62

Cancel the common factor of 2.

Cancel the common factor.

2d2=62

Divide d by 1.

d=62

d=62

Divide 6 by 2.

d=3

d=3

Solve for d 2/d+1/4=11/12