Solve 1-7/6v<9/8-5/6v

$$1 - \frac { 7 } { 6 } v < \frac { 9 } { 8 } - \frac { 5 } { 6 } v$$

Solve for v

$$v>-\frac{3}{8}$$

Solution Steps

Add \frac{5}{6}v to both sides.

$$1-\frac{7}{6}v+\frac{5}{6}v<\frac{9}{8}$$

Combine -\frac{7}{6}v and \frac{5}{6}v to get -\frac{1}{3}v.

$$1-\frac{1}{3}v<\frac{9}{8}$$

Subtract 1 from both sides.

$$-\frac{1}{3}v<\frac{9}{8}-1$$

Convert 1 to fraction \frac{8}{8}.

$$-\frac{1}{3}v<\frac{9}{8}-\frac{8}{8}$$

Since \frac{9}{8} and \frac{8}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}v<\frac{9-8}{8}$$

Subtract 8 from 9 to get 1.

$$-\frac{1}{3}v<\frac{1}{8}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}. Since -\frac{1}{3} is negative, the inequality direction is changed.

$$v>\frac{1}{8}\left(-3\right)$$

Multiply \frac{1}{8} and -3 to get \frac{-3}{8}.

$$v>\frac{-3}{8}$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$v>-\frac{3}{8}$$