Solve 5/6x-1>7x-4/3

$$\frac { 5 } { 6 } x - 1 > 7 x - \frac { 4 } { 3 }$$

Solve for x

$$x<\frac{2}{37}$$

Solution Steps

Subtract 7x from both sides.

$$\frac{5}{6}x-1-7x>-\frac{4}{3}$$

Combine \frac{5}{6}x and -7x to get -\frac{37}{6}x.

$$-\frac{37}{6}x-1>-\frac{4}{3}$$

Add 1 to both sides.

$$-\frac{37}{6}x>-\frac{4}{3}+1$$

Convert 1 to fraction \frac{3}{3}.

$$-\frac{37}{6}x>-\frac{4}{3}+\frac{3}{3}$$

Since -\frac{4}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$-\frac{37}{6}x>\frac{-4+3}{3}$$

Add -4 and 3 to get -1.

$$-\frac{37}{6}x>-\frac{1}{3}$$

Multiply both sides by -\frac{6}{37}, the reciprocal of -\frac{37}{6}. Since -\frac{37}{6} is negative, the inequality direction is changed.

$$x<-\frac{1}{3}\left(-\frac{6}{37}\right)$$

Multiply -\frac{1}{3} times -\frac{6}{37} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{-\left(-6\right)}{3\times 37}$$

Do the multiplications in the fraction \frac{-\left(-6\right)}{3\times 37}.

$$x<\frac{6}{111}$$

Reduce the fraction \frac{6}{111} to lowest terms by extracting and canceling out 3.

$$x<\frac{2}{37}$$