Solve 1197/5-(5x-41/2):111/4=814/15

$$119 \frac { 7 } { 5 } - ( 5 x - 4 \frac { 1 } { 2 } ) : 11 \frac { 1 } { 4 } = 8 \frac { 14 } { 15 }$$

Solve for x

$$x = \frac{2517}{10} = 251\frac{7}{10} = 251.7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,15.

$$3\left(119\times 5+7\right)-\frac{4}{3}\left(5x-\frac{4\times 2+1}{2}\right)=8\times 15+14$$

Multiply 119 and 5 to get 595.

$$3\left(595+7\right)-\frac{4}{3}\left(5x-\frac{4\times 2+1}{2}\right)=8\times 15+14$$

Add 595 and 7 to get 602.

$$3\times 602-\frac{4}{3}\left(5x-\frac{4\times 2+1}{2}\right)=8\times 15+14$$

Multiply 3 and 602 to get 1806.

$$1806-\frac{4}{3}\left(5x-\frac{4\times 2+1}{2}\right)=8\times 15+14$$

Multiply 4 and 2 to get 8.

$$1806-\frac{4}{3}\left(5x-\frac{8+1}{2}\right)=8\times 15+14$$

Add 8 and 1 to get 9.

$$1806-\frac{4}{3}\left(5x-\frac{9}{2}\right)=8\times 15+14$$

Use the distributive property to multiply -\frac{4}{3} by 5x-\frac{9}{2}.

$$1806-\frac{4}{3}\times 5x-\frac{4}{3}\left(-\frac{9}{2}\right)=8\times 15+14$$

Express -\frac{4}{3}\times 5 as a single fraction.

$$1806+\frac{-4\times 5}{3}x-\frac{4}{3}\left(-\frac{9}{2}\right)=8\times 15+14$$

Multiply -4 and 5 to get -20.

$$1806+\frac{-20}{3}x-\frac{4}{3}\left(-\frac{9}{2}\right)=8\times 15+14$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$1806-\frac{20}{3}x-\frac{4}{3}\left(-\frac{9}{2}\right)=8\times 15+14$$

Multiply -\frac{4}{3} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$1806-\frac{20}{3}x+\frac{-4\left(-9\right)}{3\times 2}=8\times 15+14$$

Do the multiplications in the fraction \frac{-4\left(-9\right)}{3\times 2}.

$$1806-\frac{20}{3}x+\frac{36}{6}=8\times 15+14$$

Divide 36 by 6 to get 6.

$$1806-\frac{20}{3}x+6=8\times 15+14$$

Add 1806 and 6 to get 1812.

$$1812-\frac{20}{3}x=8\times 15+14$$

Multiply 8 and 15 to get 120.

$$1812-\frac{20}{3}x=120+14$$

Add 120 and 14 to get 134.

$$1812-\frac{20}{3}x=134$$

Subtract 1812 from both sides.

$$-\frac{20}{3}x=134-1812$$

Subtract 1812 from 134 to get -1678.

$$-\frac{20}{3}x=-1678$$

Multiply both sides by -\frac{3}{20}, the reciprocal of -\frac{20}{3}.

$$x=-1678\left(-\frac{3}{20}\right)$$

Express -1678\left(-\frac{3}{20}\right) as a single fraction.

$$x=\frac{-1678\left(-3\right)}{20}$$

Multiply -1678 and -3 to get 5034.

$$x=\frac{5034}{20}$$

Reduce the fraction \frac{5034}{20} to lowest terms by extracting and canceling out 2.

$$x=\frac{2517}{10}$$