Solve 5/12x-13/9=-7/2x-7/10

$$\frac{ 5 }{ 12 } x- \frac{ 13 }{ 9 } =- \frac{ 7 }{ 2 } x- \frac{ 7 }{ 10 }$$

Solve for x

$$x=\frac{134}{705}\approx 0.190070922$$

Steps for Solving Linear Equation

Add \frac{7}{2}x to both sides.

$$\frac{5}{12}x-\frac{13}{9}+\frac{7}{2}x=-\frac{7}{10}$$

Combine \frac{5}{12}x and \frac{7}{2}x to get \frac{47}{12}x.

$$\frac{47}{12}x-\frac{13}{9}=-\frac{7}{10}$$

Add \frac{13}{9} to both sides.

$$\frac{47}{12}x=-\frac{7}{10}+\frac{13}{9}$$

Least common multiple of 10 and 9 is 90. Convert -\frac{7}{10} and \frac{13}{9} to fractions with denominator 90.

$$\frac{47}{12}x=-\frac{63}{90}+\frac{130}{90}$$

Since -\frac{63}{90} and \frac{130}{90} have the same denominator, add them by adding their numerators.

$$\frac{47}{12}x=\frac{-63+130}{90}$$

Add -63 and 130 to get 67.

$$\frac{47}{12}x=\frac{67}{90}$$

Multiply both sides by \frac{12}{47}, the reciprocal of \frac{47}{12}.

$$x=\frac{67}{90}\times \frac{12}{47}$$

Multiply \frac{67}{90} times \frac{12}{47} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{67\times 12}{90\times 47}$$

Do the multiplications in the fraction \frac{67\times 12}{90\times 47}.

$$x=\frac{804}{4230}$$

Reduce the fraction \frac{804}{4230} to lowest terms by extracting and canceling out 6.

$$x=\frac{134}{705}$$