Solve b-4/5>6/5b-3

$$b - \frac { 4 } { 5 } > \frac { 6 } { 5 } b - 3$$

Solve for b

$$b<11$$

Solution Steps

Subtract \frac{6}{5}b from both sides.

$$b-\frac{4}{5}-\frac{6}{5}b>-3$$

Combine b and -\frac{6}{5}b to get -\frac{1}{5}b.

$$-\frac{1}{5}b-\frac{4}{5}>-3$$

Add \frac{4}{5} to both sides.

$$-\frac{1}{5}b>-3+\frac{4}{5}$$

Convert -3 to fraction -\frac{15}{5}.

$$-\frac{1}{5}b>-\frac{15}{5}+\frac{4}{5}$$

Since -\frac{15}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1}{5}b>\frac{-15+4}{5}$$

Add -15 and 4 to get -11.

$$-\frac{1}{5}b>-\frac{11}{5}$$

Multiply both sides by -5, the reciprocal of -\frac{1}{5}. Since -\frac{1}{5} is negative, the inequality direction is changed.

$$b<-\frac{11}{5}\left(-5\right)$$

Express -\frac{11}{5}\left(-5\right) as a single fraction.

$$b<\frac{-11\left(-5\right)}{5}$$

Multiply -11 and -5 to get 55.

$$b<\frac{55}{5}$$

Divide 55 by 5 to get 11.

$$b<11$$