Solve -1/3(x-1)=-1/6-x-1/5

$$- \frac { 1 } { 3 } ( x - 1 ) = - \frac { 1 } { 6 } - \frac { x - 1 } { 5 }$$

Solve for x

$$x = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,6,5.

$$-10\left(x-1\right)=-5-6\left(x-1\right)$$

Use the distributive property to multiply -10 by x-1.

$$-10x+10=-5-6\left(x-1\right)$$

Use the distributive property to multiply -6 by x-1.

$$-10x+10=-5-6x+6$$

Add -5 and 6 to get 1.

$$-10x+10=1-6x$$

Add 6x to both sides.

$$-10x+10+6x=1$$

Combine -10x and 6x to get -4x.

$$-4x+10=1$$

Subtract 10 from both sides.

$$-4x=1-10$$

Subtract 10 from 1 to get -9.

$$-4x=-9$$

Divide both sides by -4.

$$x=\frac{-9}{-4}$$

Fraction \frac{-9}{-4} can be simplified to \frac{9}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{9}{4}$$