Solve 3-4x/5-x-1/6=4+x/3-16/9

$$\frac { 3 - 4 x } { 5 } - \frac { x - 1 } { 6 } = \frac { 4 + x } { 3 } - \frac { 16 } { 9 }$$

Solve for x

$$x=\frac{109}{117}\approx 0.931623932$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 5,6,3,9.

$$18\left(3-4x\right)-15\left(x-1\right)=30\left(4+x\right)-160$$

Use the distributive property to multiply 18 by 3-4x.

$$54-72x-15\left(x-1\right)=30\left(4+x\right)-160$$

Use the distributive property to multiply -15 by x-1.

$$54-72x-15x+15=30\left(4+x\right)-160$$

Combine -72x and -15x to get -87x.

$$54-87x+15=30\left(4+x\right)-160$$

Add 54 and 15 to get 69.

$$69-87x=30\left(4+x\right)-160$$

Use the distributive property to multiply 30 by 4+x.

$$69-87x=120+30x-160$$

Subtract 160 from 120 to get -40.

$$69-87x=-40+30x$$

Subtract 30x from both sides.

$$69-87x-30x=-40$$

Combine -87x and -30x to get -117x.

$$69-117x=-40$$

Subtract 69 from both sides.

$$-117x=-40-69$$

Subtract 69 from -40 to get -109.

$$-117x=-109$$

Divide both sides by -117.

$$x=\frac{-109}{-117}$$

Fraction \frac{-109}{-117} can be simplified to \frac{109}{117} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{109}{117}$$