Solve 1/2(x-2)>1/4(7x-2)

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

Solve for x

$$x<-\frac{2}{5}$$

Solution Steps

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

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

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

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

Divide -2 by 2 to get -1.

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

Use the distributive property to multiply \frac{1}{4} by 7x-2.

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

Multiply \frac{1}{4} and 7 to get \frac{7}{4}.

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

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

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

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

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

Subtract \frac{7}{4}x from both sides.

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

Combine \frac{1}{2}x and -\frac{7}{4}x to get -\frac{5}{4}x.

$$-\frac{5}{4}x-1>-\frac{1}{2}$$

Add 1 to both sides.

$$-\frac{5}{4}x>-\frac{1}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$-\frac{5}{4}x>-\frac{1}{2}+\frac{2}{2}$$

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

$$-\frac{5}{4}x>\frac{-1+2}{2}$$

Add -1 and 2 to get 1.

$$-\frac{5}{4}x>\frac{1}{2}$$

Multiply both sides by -\frac{4}{5}, the reciprocal of -\frac{5}{4}. Since -\frac{5}{4} is negative, the inequality direction is changed.

$$x<\frac{1}{2}\left(-\frac{4}{5}\right)$$

Multiply \frac{1}{2} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{1\left(-4\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{1\left(-4\right)}{2\times 5}.

$$x<\frac{-4}{10}$$

Reduce the fraction \frac{-4}{10} to lowest terms by extracting and canceling out 2.

$$x<-\frac{2}{5}$$