Solve 1w-1/3+5+3w/2=5w-6

$$\frac { 1 w - 1 } { 3 } + \frac { 5 + 3 w } { 2 } = 5 w - 6$$

Solve for w

$$w = \frac{49}{19} = 2\frac{11}{19} \approx 2.578947368$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\left(1w-1\right)+3\left(5+3w\right)=30w-36$$

Use the distributive property to multiply 2 by 1w-1.

$$2w-2+3\left(5+3w\right)=30w-36$$

Use the distributive property to multiply 3 by 5+3w.

$$2w-2+15+9w=30w-36$$

Add -2 and 15 to get 13.

$$2w+13+9w=30w-36$$

Combine 2w and 9w to get 11w.

$$11w+13=30w-36$$

Subtract 30w from both sides.

$$11w+13-30w=-36$$

Combine 11w and -30w to get -19w.

$$-19w+13=-36$$

Subtract 13 from both sides.

$$-19w=-36-13$$

Subtract 13 from -36 to get -49.

$$-19w=-49$$

Divide both sides by -19.

$$w=\frac{-49}{-19}$$

Fraction \frac{-49}{-19} can be simplified to \frac{49}{19} by removing the negative sign from both the numerator and the denominator.

$$w=\frac{49}{19}$$