Solve 3/2-1-x/3-(2x+1/2+5x)=2x-x-2/2

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

Solve for x

$$x=-\frac{2}{43}\approx -0.046511628$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$6\left(\frac{3}{2}-\frac{1-x}{3}\right)-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{3}{2} times \frac{3}{3}. Multiply \frac{1-x}{3} times \frac{2}{2}.

$$6\left(\frac{3\times 3}{6}-\frac{2\left(1-x\right)}{6}\right)-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

Since \frac{3\times 3}{6} and \frac{2\left(1-x\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$6\times \frac{3\times 3-2\left(1-x\right)}{6}-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

Do the multiplications in 3\times 3-2\left(1-x\right).

$$6\times \frac{9-2+2x}{6}-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

Combine like terms in 9-2+2x.

$$6\times \frac{7+2x}{6}-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

Express 6\times \frac{7+2x}{6} as a single fraction.

$$\frac{6\left(7+2x\right)}{6}-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

Cancel out 6 and 6.

$$7+2x-6\left(\frac{2x+1}{2}+5x\right)=12x-3\left(x-2\right)$$

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

$$7+2x-6\left(\frac{2x+1}{2}+5x\right)=12x-3x+6$$

Combine 12x and -3x to get 9x.

$$7+2x-6\left(\frac{2x+1}{2}+5x\right)=9x+6$$

Divide each term of 2x+1 by 2 to get x+\frac{1}{2}.

$$7+2x-6\left(x+\frac{1}{2}+5x\right)=9x+6$$

Combine x and 5x to get 6x.

$$7+2x-6\left(6x+\frac{1}{2}\right)=9x+6$$

Use the distributive property to multiply -6 by 6x+\frac{1}{2}.

$$7+2x-36x-6\times \frac{1}{2}=9x+6$$

Multiply -6 and \frac{1}{2} to get \frac{-6}{2}.

$$7+2x-36x+\frac{-6}{2}=9x+6$$

Divide -6 by 2 to get -3.

$$7+2x-36x-3=9x+6$$

Combine 2x and -36x to get -34x.

$$7-34x-3=9x+6$$

Subtract 3 from 7 to get 4.

$$4-34x=9x+6$$

Subtract 9x from both sides.

$$4-34x-9x=6$$

Combine -34x and -9x to get -43x.

$$4-43x=6$$

Subtract 4 from both sides.

$$-43x=6-4$$

Subtract 4 from 6 to get 2.

$$-43x=2$$

Divide both sides by -43.

$$x=\frac{2}{-43}$$

Fraction \frac{2}{-43} can be rewritten as -\frac{2}{43} by extracting the negative sign.

$$x=-\frac{2}{43}$$