Solve x-1-1.5x/6+x/2=x-1

$$x - \frac { 1 - 1.5 x } { 6 } + \frac { x } { 2 } = x - 1$$

Solve for x

$$x = -\frac{10}{9} = -1\frac{1}{9} \approx -1.111111111$$

Steps for Solving Linear Equation

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

$$6x-\left(1-1.5x\right)+3x=6x-6$$

To find the opposite of 1-1.5x, find the opposite of each term.

$$6x-1-\left(-1.5x\right)+3x=6x-6$$

The opposite of -1.5x is 1.5x.

$$6x-1+1.5x+3x=6x-6$$

Combine 6x and 1.5x to get 7.5x.

$$7.5x-1+3x=6x-6$$

Combine 7.5x and 3x to get 10.5x.

$$10.5x-1=6x-6$$

Subtract 6x from both sides.

$$10.5x-1-6x=-6$$

Combine 10.5x and -6x to get 4.5x.

$$4.5x-1=-6$$

Add 1 to both sides.

$$4.5x=-6+1$$

Add -6 and 1 to get -5.

$$4.5x=-5$$

Divide both sides by 4.5.

$$x=\frac{-5}{4.5}$$

Expand \frac{-5}{4.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{-50}{45}$$

Reduce the fraction \frac{-50}{45} to lowest terms by extracting and canceling out 5.

$$x=-\frac{10}{9}$$