Solve (x-1/2)-3(x+1)=2(x+1/4)

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

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x+1.

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

Combine x and -3x to get -2x.

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

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

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

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

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

Subtract 6 from -1 to get -7.

$$-2x-\frac{7}{2}=2\left(x+\frac{1}{4}\right)$$

Use the distributive property to multiply 2 by x+\frac{1}{4}.

$$-2x-\frac{7}{2}=2x+2\times \frac{1}{4}$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$-2x-\frac{7}{2}=2x+\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-2x-\frac{7}{2}=2x+\frac{1}{2}$$

Subtract 2x from both sides.

$$-2x-\frac{7}{2}-2x=\frac{1}{2}$$

Combine -2x and -2x to get -4x.

$$-4x-\frac{7}{2}=\frac{1}{2}$$

Add \frac{7}{2} to both sides.

$$-4x=\frac{1}{2}+\frac{7}{2}$$

Since \frac{1}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$-4x=\frac{1+7}{2}$$

Add 1 and 7 to get 8.

$$-4x=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$-4x=4$$

Divide both sides by -4.

$$x=\frac{4}{-4}$$

Divide 4 by -4 to get -1.

$$x=-1$$