Solve Matrix

$$\left. \begin{array} { l } { ( 5 \frac { 2 } { 3 } - 4 \frac { 1 } { 2 } ) : x = ( 8 \frac { 3 } { 4 } - 6 \frac { 2 } { 3 } ) : ( 3 \frac { 1 } { 2 } + 1 \frac { 1 } { 4 } ) } \\ { \left( \begin{array} { l l } { 1 } & { 1 } \end{array} \right) } \end{array} \right.$$

Solve for x

$$x = \frac{133}{50} = 2\frac{33}{50} = 2.66$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{5\times 3+2}{3}-\frac{4\times 2+1}{2}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Multiply 5 and 3 to get 15.

$$\frac{15+2}{3}-\frac{4\times 2+1}{2}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Add 15 and 2 to get 17.

$$\frac{17}{3}-\frac{4\times 2+1}{2}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Multiply 4 and 2 to get 8.

$$\frac{17}{3}-\frac{8+1}{2}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Add 8 and 1 to get 9.

$$\frac{17}{3}-\frac{9}{2}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{17}{3} and \frac{9}{2} to fractions with denominator 6.

$$\frac{34}{6}-\frac{27}{6}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Since \frac{34}{6} and \frac{27}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-27}{6}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Subtract 27 from 34 to get 7.

$$\frac{7}{6}=\frac{4}{19}x\left(\frac{8\times 4+3}{4}-\frac{6\times 3+2}{3}\right)$$

Multiply 8 and 4 to get 32.

$$\frac{7}{6}=\frac{4}{19}x\left(\frac{32+3}{4}-\frac{6\times 3+2}{3}\right)$$

Add 32 and 3 to get 35.

$$\frac{7}{6}=\frac{4}{19}x\left(\frac{35}{4}-\frac{6\times 3+2}{3}\right)$$

Multiply 6 and 3 to get 18.

$$\frac{7}{6}=\frac{4}{19}x\left(\frac{35}{4}-\frac{18+2}{3}\right)$$

Add 18 and 2 to get 20.

$$\frac{7}{6}=\frac{4}{19}x\left(\frac{35}{4}-\frac{20}{3}\right)$$

Least common multiple of 4 and 3 is 12. Convert \frac{35}{4} and \frac{20}{3} to fractions with denominator 12.

$$\frac{7}{6}=\frac{4}{19}x\left(\frac{105}{12}-\frac{80}{12}\right)$$

Since \frac{105}{12} and \frac{80}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}=\frac{4}{19}x\times \frac{105-80}{12}$$

Subtract 80 from 105 to get 25.

$$\frac{7}{6}=\frac{4}{19}x\times \frac{25}{12}$$

Multiply \frac{4}{19} times \frac{25}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{6}=\frac{4\times 25}{19\times 12}x$$

Do the multiplications in the fraction \frac{4\times 25}{19\times 12}.

$$\frac{7}{6}=\frac{100}{228}x$$

Reduce the fraction \frac{100}{228} to lowest terms by extracting and canceling out 4.

$$\frac{7}{6}=\frac{25}{57}x$$

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

$$\frac{25}{57}x=\frac{7}{6}$$

Multiply both sides by \frac{57}{25}, the reciprocal of \frac{25}{57}.

$$x=\frac{7}{6}\times \frac{57}{25}$$

Multiply \frac{7}{6} times \frac{57}{25} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 57}{6\times 25}$$

Do the multiplications in the fraction \frac{7\times 57}{6\times 25}.

$$x=\frac{399}{150}$$

Reduce the fraction \frac{399}{150} to lowest terms by extracting and canceling out 3.

$$x=\frac{133}{50}$$