Solve 1/2(7x-14)-2=1/4(x-2)

$$\frac { 1 } { 2 } ( 7 x - 14 ) - 2 = \frac { 1 } { 4 } ( x - 2 )$$

Solve for x

$$x = \frac{34}{13} = 2\frac{8}{13} \approx 2.615384615$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by 7x-14.

$$\frac{1}{2}\times 7x+\frac{1}{2}\left(-14\right)-2=\frac{1}{4}\left(x-2\right)$$

Multiply \frac{1}{2} and 7 to get \frac{7}{2}.

$$\frac{7}{2}x+\frac{1}{2}\left(-14\right)-2=\frac{1}{4}\left(x-2\right)$$

Multiply \frac{1}{2} and -14 to get \frac{-14}{2}.

$$\frac{7}{2}x+\frac{-14}{2}-2=\frac{1}{4}\left(x-2\right)$$

Divide -14 by 2 to get -7.

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

Subtract 2 from -7 to get -9.

$$\frac{7}{2}x-9=\frac{1}{4}\left(x-2\right)$$

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

$$\frac{7}{2}x-9=\frac{1}{4}x+\frac{1}{4}\left(-2\right)$$

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

$$\frac{7}{2}x-9=\frac{1}{4}x+\frac{-2}{4}$$

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

$$\frac{7}{2}x-9=\frac{1}{4}x-\frac{1}{2}$$

Subtract \frac{1}{4}x from both sides.

$$\frac{7}{2}x-9-\frac{1}{4}x=-\frac{1}{2}$$

Combine \frac{7}{2}x and -\frac{1}{4}x to get \frac{13}{4}x.

$$\frac{13}{4}x-9=-\frac{1}{2}$$

Add 9 to both sides.

$$\frac{13}{4}x=-\frac{1}{2}+9$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{13}{4}x=-\frac{1}{2}+\frac{18}{2}$$

Since -\frac{1}{2} and \frac{18}{2} have the same denominator, add them by adding their numerators.

$$\frac{13}{4}x=\frac{-1+18}{2}$$

Add -1 and 18 to get 17.

$$\frac{13}{4}x=\frac{17}{2}$$

Multiply both sides by \frac{4}{13}, the reciprocal of \frac{13}{4}.

$$x=\frac{17}{2}\times \frac{4}{13}$$

Multiply \frac{17}{2} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{17\times 4}{2\times 13}$$

Do the multiplications in the fraction \frac{17\times 4}{2\times 13}.

$$x=\frac{68}{26}$$

Reduce the fraction \frac{68}{26} to lowest terms by extracting and canceling out 2.

$$x=\frac{34}{13}$$