Solve 21/6-42/3+x=37/16

$$2 \frac { 1 } { 6 } - 4 \frac { 2 } { 3 } + x = 3 \frac { 7 } { 16 }$$

Solve for x

$$x = \frac{95}{16} = 5\frac{15}{16} = 5.9375$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 48, the least common multiple of 6,3,16.

$$8\left(2\times 6+1\right)-16\left(4\times 3+2\right)+48x=3\left(3\times 16+7\right)$$

Multiply 2 and 6 to get 12.

$$8\left(12+1\right)-16\left(4\times 3+2\right)+48x=3\left(3\times 16+7\right)$$

Add 12 and 1 to get 13.

$$8\times 13-16\left(4\times 3+2\right)+48x=3\left(3\times 16+7\right)$$

Multiply 8 and 13 to get 104.

$$104-16\left(4\times 3+2\right)+48x=3\left(3\times 16+7\right)$$

Multiply 4 and 3 to get 12.

$$104-16\left(12+2\right)+48x=3\left(3\times 16+7\right)$$

Add 12 and 2 to get 14.

$$104-16\times 14+48x=3\left(3\times 16+7\right)$$

Multiply -16 and 14 to get -224.

$$104-224+48x=3\left(3\times 16+7\right)$$

Subtract 224 from 104 to get -120.

$$-120+48x=3\left(3\times 16+7\right)$$

Multiply 3 and 16 to get 48.

$$-120+48x=3\left(48+7\right)$$

Add 48 and 7 to get 55.

$$-120+48x=3\times 55$$

Multiply 3 and 55 to get 165.

$$-120+48x=165$$

Add 120 to both sides.

$$48x=165+120$$

Add 165 and 120 to get 285.

$$48x=285$$

Divide both sides by 48.

$$x=\frac{285}{48}$$

Reduce the fraction \frac{285}{48} to lowest terms by extracting and canceling out 3.

$$x=\frac{95}{16}$$