Solve 3x/10-x+1/5=x+3/2+2x+3/5-1frac{1}{10}

$$\frac { 3 x } { 10 } - \frac { x + 1 } { 5 } = \frac { x + 3 } { 2 } + \frac { 2 x + 3 } { 5 } - 1 \frac { 1 } { 10 }$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

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

$$3x-2\left(x+1\right)=5\left(x+3\right)+2\left(2x+3\right)-\left(1\times 10+1\right)$$

Use the distributive property to multiply -2 by x+1.

$$3x-2x-2=5\left(x+3\right)+2\left(2x+3\right)-\left(1\times 10+1\right)$$

Combine 3x and -2x to get x.

$$x-2=5\left(x+3\right)+2\left(2x+3\right)-\left(1\times 10+1\right)$$

Use the distributive property to multiply 5 by x+3.

$$x-2=5x+15+2\left(2x+3\right)-\left(1\times 10+1\right)$$

Use the distributive property to multiply 2 by 2x+3.

$$x-2=5x+15+4x+6-\left(1\times 10+1\right)$$

Combine 5x and 4x to get 9x.

$$x-2=9x+15+6-\left(1\times 10+1\right)$$

Add 15 and 6 to get 21.

$$x-2=9x+21-\left(1\times 10+1\right)$$

Multiply 1 and 10 to get 10.

$$x-2=9x+21-\left(10+1\right)$$

Add 10 and 1 to get 11.

$$x-2=9x+21-11$$

Subtract 11 from 21 to get 10.

$$x-2=9x+10$$

Subtract 9x from both sides.

$$x-2-9x=10$$

Combine x and -9x to get -8x.

$$-8x-2=10$$

Add 2 to both sides.

$$-8x=10+2$$

Add 10 and 2 to get 12.

$$-8x=12$$

Divide both sides by -8.

$$x=\frac{12}{-8}$$

Reduce the fraction \frac{12}{-8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{3}{2}$$