Solve 7/8x+6/3>1/6x+6/4

$$\frac { 7 } { 8 } x + \frac { 6 } { 3 } > \frac { 1 } { 6 } x + \frac { 6 } { 4 }$$

Solve for x

$$x>-\frac{12}{17}$$

Solution Steps

Divide 6 by 3 to get 2.

$$\frac{7}{8}x+2>\frac{1}{6}x+\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{7}{8}x+2>\frac{1}{6}x+\frac{3}{2}$$

Subtract \frac{1}{6}x from both sides.

$$\frac{7}{8}x+2-\frac{1}{6}x>\frac{3}{2}$$

Combine \frac{7}{8}x and -\frac{1}{6}x to get \frac{17}{24}x.

$$\frac{17}{24}x+2>\frac{3}{2}$$

Subtract 2 from both sides.

$$\frac{17}{24}x>\frac{3}{2}-2$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{17}{24}x>\frac{3}{2}-\frac{4}{2}$$

Since \frac{3}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{24}x>\frac{3-4}{2}$$

Subtract 4 from 3 to get -1.

$$\frac{17}{24}x>-\frac{1}{2}$$

Multiply both sides by \frac{24}{17}, the reciprocal of \frac{17}{24}. Since \frac{17}{24} is positive, the inequality direction remains the same.

$$x>-\frac{1}{2}\times \frac{24}{17}$$

Multiply -\frac{1}{2} times \frac{24}{17} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-24}{2\times 17}$$

Do the multiplications in the fraction \frac{-24}{2\times 17}.

$$x>\frac{-24}{34}$$

Reduce the fraction \frac{-24}{34} to lowest terms by extracting and canceling out 2.

$$x>-\frac{12}{17}$$