Solve 5x-(2x/3+x/2)=1/3(9x-1/2)

$$5 x - ( \frac { 2 x } { 3 } + \frac { x } { 2 } ) = \frac { 1 } { 3 } ( 9 x - \frac { 1 } { 2 } )$$

Solve for x

$$x=-\frac{1}{5}=-0.2$$

Steps for Solving Linear Equation

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

$$30x-6\left(\frac{2x}{3}+\frac{x}{2}\right)=2\left(9x-\frac{1}{2}\right)$$

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

$$30x-6\left(\frac{2\times 2x}{6}+\frac{3x}{6}\right)=2\left(9x-\frac{1}{2}\right)$$

Since \frac{2\times 2x}{6} and \frac{3x}{6} have the same denominator, add them by adding their numerators.

$$30x-6\times \frac{2\times 2x+3x}{6}=2\left(9x-\frac{1}{2}\right)$$

Do the multiplications in 2\times 2x+3x.

$$30x-6\times \frac{4x+3x}{6}=2\left(9x-\frac{1}{2}\right)$$

Combine like terms in 4x+3x.

$$30x-6\times \frac{7x}{6}=2\left(9x-\frac{1}{2}\right)$$

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

$$30x-\frac{6\times 7x}{6}=2\left(9x-\frac{1}{2}\right)$$

Cancel out 6 and 6.

$$30x-7x=2\left(9x-\frac{1}{2}\right)$$

Combine 30x and -7x to get 23x.

$$23x=2\left(9x-\frac{1}{2}\right)$$

Use the distributive property to multiply 2 by 9x-\frac{1}{2}.

$$23x=18x+2\left(-\frac{1}{2}\right)$$

Cancel out 2 and 2.

$$23x=18x-1$$

Subtract 18x from both sides.

$$23x-18x=-1$$

Combine 23x and -18x to get 5x.

$$5x=-1$$

Divide both sides by 5.

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

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

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