Solve -12/16=-10/6+17/13b

$$- \frac { 12 } { 16 } = - \frac { 10 } { 6 } + \frac { 17 } { 13 } b$$

Solve for b

$$b=\frac{143}{204}\approx 0.700980392$$

Steps for Solving Linear Equation

Reduce the fraction \frac{12}{16} to lowest terms by extracting and canceling out 4.

$$-\frac{3}{4}=-\frac{10}{6}+\frac{17}{13}b$$

Reduce the fraction \frac{10}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{4}=-\frac{5}{3}+\frac{17}{13}b$$

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

$$-\frac{5}{3}+\frac{17}{13}b=-\frac{3}{4}$$

Add \frac{5}{3} to both sides.

$$\frac{17}{13}b=-\frac{3}{4}+\frac{5}{3}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{5}{3} to fractions with denominator 12.

$$\frac{17}{13}b=-\frac{9}{12}+\frac{20}{12}$$

Since -\frac{9}{12} and \frac{20}{12} have the same denominator, add them by adding their numerators.

$$\frac{17}{13}b=\frac{-9+20}{12}$$

Add -9 and 20 to get 11.

$$\frac{17}{13}b=\frac{11}{12}$$

Multiply both sides by \frac{13}{17}, the reciprocal of \frac{17}{13}.

$$b=\frac{11}{12}\times \frac{13}{17}$$

Multiply \frac{11}{12} times \frac{13}{17} by multiplying numerator times numerator and denominator times denominator.

$$b=\frac{11\times 13}{12\times 17}$$

Do the multiplications in the fraction \frac{11\times 13}{12\times 17}.

$$b=\frac{143}{204}$$