Solve 22/7*3/2*3/2*14=(22/7*frac{11}{2}*frac{11}{2}*14)-(frac{22}{7}*frac{3}{2}*frac{3}{2}*h)

$$\frac { 22 } { 7 } \times \frac { 3 } { 2 } \times \frac { 3 } { 2 } \times 14 = ( \frac { 22 } { 7 } \times \frac { 11 } { 2 } \times \frac { 11 } { 2 } \times 14 ) - ( \frac { 22 } { 7 } \times \frac { 3 } { 2 } \times \frac { 3 } { 2 } \times h )$$

Solve for h

$$h = \frac{1568}{9} = 174\frac{2}{9} \approx 174.222222222$$

Steps for Solving Linear Equation

Multiply \frac{22}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 3}{7\times 2}\times \frac{3}{2}\times 14=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Do the multiplications in the fraction \frac{22\times 3}{7\times 2}.

$$\frac{66}{14}\times \frac{3}{2}\times 14=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Reduce the fraction \frac{66}{14} to lowest terms by extracting and canceling out 2.

$$\frac{33}{7}\times \frac{3}{2}\times 14=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Multiply \frac{33}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 3}{7\times 2}\times 14=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Do the multiplications in the fraction \frac{33\times 3}{7\times 2}.

$$\frac{99}{14}\times 14=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Cancel out 14 and 14.

$$99=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Multiply \frac{22}{7} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$99=\frac{22\times 11}{7\times 2}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Do the multiplications in the fraction \frac{22\times 11}{7\times 2}.

$$99=\frac{242}{14}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Reduce the fraction \frac{242}{14} to lowest terms by extracting and canceling out 2.

$$99=\frac{121}{7}\times \frac{11}{2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Multiply \frac{121}{7} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$99=\frac{121\times 11}{7\times 2}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Do the multiplications in the fraction \frac{121\times 11}{7\times 2}.

$$99=\frac{1331}{14}\times 14-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Cancel out 14 and 14.

$$99=1331-\frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}h$$

Multiply \frac{22}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$99=1331-\frac{22\times 3}{7\times 2}\times \frac{3}{2}h$$

Do the multiplications in the fraction \frac{22\times 3}{7\times 2}.

$$99=1331-\frac{66}{14}\times \frac{3}{2}h$$

Reduce the fraction \frac{66}{14} to lowest terms by extracting and canceling out 2.

$$99=1331-\frac{33}{7}\times \frac{3}{2}h$$

Multiply \frac{33}{7} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$99=1331-\frac{33\times 3}{7\times 2}h$$

Do the multiplications in the fraction \frac{33\times 3}{7\times 2}.

$$99=1331-\frac{99}{14}h$$

Swap sides so that all variable terms are on the left hand side.

$$1331-\frac{99}{14}h=99$$

Subtract 1331 from both sides.

$$-\frac{99}{14}h=99-1331$$

Subtract 1331 from 99 to get -1232.

$$-\frac{99}{14}h=-1232$$

Multiply both sides by -\frac{14}{99}, the reciprocal of -\frac{99}{14}.

$$h=-1232\left(-\frac{14}{99}\right)$$

Express -1232\left(-\frac{14}{99}\right) as a single fraction.

$$h=\frac{-1232\left(-14\right)}{99}$$

Multiply -1232 and -14 to get 17248.

$$h=\frac{17248}{99}$$

Reduce the fraction \frac{17248}{99} to lowest terms by extracting and canceling out 11.

$$h=\frac{1568}{9}$$