Solve 1/2(x/2+1)-2x/3=1/6(x-frac{1}{2})

$$\frac { 1 } { 2 } ( \frac { x } { 2 } + 1 ) - \frac { 2 x } { 3 } = \frac { 1 } { 6 } ( x - \frac { 1 } { 2 } )$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 3 by \frac{x}{2}+1.

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

Express 3\times \frac{x}{2} as a single fraction.

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

Multiply -2 and 2 to get -4.

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

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

$$\frac{3x}{2}+3-4x=x-\frac{1}{2}$$

Subtract x from both sides.

$$\frac{3x}{2}+3-4x-x=-\frac{1}{2}$$

Combine -4x and -x to get -5x.

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

Subtract 3 from both sides.

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

Convert 3 to fraction \frac{6}{2}.

$$\frac{3x}{2}-5x=-\frac{1}{2}-\frac{6}{2}$$

Since -\frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x}{2}-5x=\frac{-1-6}{2}$$

Subtract 6 from -1 to get -7.

$$\frac{3x}{2}-5x=-\frac{7}{2}$$

Multiply both sides of the equation by 2.

$$3x-10x=-7$$

Combine 3x and -10x to get -7x.

$$-7x=-7$$

Divide both sides by -7.

$$x=\frac{-7}{-7}$$

Divide -7 by -7 to get 1.

$$x=1$$