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

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

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 6,3,9.

$$3\left(x-1\right)=6\left(4+x\right)-32$$

Use the distributive property to multiply 3 by x-1.

$$3x-3=6\left(4+x\right)-32$$

Use the distributive property to multiply 6 by 4+x.

$$3x-3=24+6x-32$$

Subtract 32 from 24 to get -8.

$$3x-3=-8+6x$$

Subtract 6x from both sides.

$$3x-3-6x=-8$$

Combine 3x and -6x to get -3x.

$$-3x-3=-8$$

Add 3 to both sides.

$$-3x=-8+3$$

Add -8 and 3 to get -5.

$$-3x=-5$$

Divide both sides by -3.

$$x=\frac{-5}{-3}$$

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{3}$$