Solve 9x/5-6x-3/15-4x-2/10=x-1/2+frac{3}{10}

$$\frac { 9 x } { 5 } - \frac { 6 x - 3 } { 15 } - \frac { 4 x - 2 } { 10 } = \frac { x - 1 } { 2 } + \frac { 3 } { 10 }$$

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,15,10,2.

$$6\times 9x-2\left(6x-3\right)-3\left(4x-2\right)=15\left(x-1\right)+9$$

Multiply 6 and 9 to get 54.

$$54x-2\left(6x-3\right)-3\left(4x-2\right)=15\left(x-1\right)+9$$

Use the distributive property to multiply -2 by 6x-3.

$$54x-12x+6-3\left(4x-2\right)=15\left(x-1\right)+9$$

Combine 54x and -12x to get 42x.

$$42x+6-3\left(4x-2\right)=15\left(x-1\right)+9$$

Use the distributive property to multiply -3 by 4x-2.

$$42x+6-12x+6=15\left(x-1\right)+9$$

Combine 42x and -12x to get 30x.

$$30x+6+6=15\left(x-1\right)+9$$

Add 6 and 6 to get 12.

$$30x+12=15\left(x-1\right)+9$$

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

$$30x+12=15x-15+9$$

Add -15 and 9 to get -6.

$$30x+12=15x-6$$

Subtract 15x from both sides.

$$30x+12-15x=-6$$

Combine 30x and -15x to get 15x.

$$15x+12=-6$$

Subtract 12 from both sides.

$$15x=-6-12$$

Subtract 12 from -6 to get -18.

$$15x=-18$$

Divide both sides by 15.

$$x=\frac{-18}{15}$$

Reduce the fraction \frac{-18}{15} to lowest terms by extracting and canceling out 3.

$$x=-\frac{6}{5}$$