Solve -95/6b+23/4b+15/12b=17/27

$$- 9 \frac { 5 } { 6 } b + 2 \frac { 3 } { 4 } b + 1 \frac { 5 } { 12 } b = 1 \frac { 7 } { 27 }$$

Solve for b

$$b=-\frac{2}{9}\approx -0.222222222$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 108, the least common multiple of 6,4,12,27.

$$108\left(-\frac{9\times 6+5}{6}\right)b+27\left(2\times 4+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Multiply 9 and 6 to get 54.

$$108\left(-\frac{54+5}{6}\right)b+27\left(2\times 4+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Add 54 and 5 to get 59.

$$108\left(-\frac{59}{6}\right)b+27\left(2\times 4+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Express 108\left(-\frac{59}{6}\right) as a single fraction.

$$\frac{108\left(-59\right)}{6}b+27\left(2\times 4+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Multiply 108 and -59 to get -6372.

$$\frac{-6372}{6}b+27\left(2\times 4+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Divide -6372 by 6 to get -1062.

$$-1062b+27\left(2\times 4+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Multiply 2 and 4 to get 8.

$$-1062b+27\left(8+3\right)b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Add 8 and 3 to get 11.

$$-1062b+27\times 11b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Multiply 27 and 11 to get 297.

$$-1062b+297b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Combine -1062b and 297b to get -765b.

$$-765b+9\left(1\times 12+5\right)b=4\left(1\times 27+7\right)$$

Multiply 1 and 12 to get 12.

$$-765b+9\left(12+5\right)b=4\left(1\times 27+7\right)$$

Add 12 and 5 to get 17.

$$-765b+9\times 17b=4\left(1\times 27+7\right)$$

Multiply 9 and 17 to get 153.

$$-765b+153b=4\left(1\times 27+7\right)$$

Combine -765b and 153b to get -612b.

$$-612b=4\left(1\times 27+7\right)$$

Multiply 1 and 27 to get 27.

$$-612b=4\left(27+7\right)$$

Add 27 and 7 to get 34.

$$-612b=4\times 34$$

Multiply 4 and 34 to get 136.

$$-612b=136$$

Divide both sides by -612.

$$b=\frac{136}{-612}$$

Reduce the fraction \frac{136}{-612} to lowest terms by extracting and canceling out 68.

$$b=-\frac{2}{9}$$