Solve the Inequality for y 4/3<-8/3y

$\frac{4}{3} < - \frac{8}{3} y$

Rewrite so $y$ is on the left side of the inequality.

$- \frac{8}{3} y > \frac{4}{3}$

Multiply each term in $- \frac{8}{3} y > \frac{4}{3}$ by $- \frac{3}{8}$ to eliminate the fractions.

Multiply each term in $- \frac{8}{3} y > \frac{4}{3}$ by $- \frac{3}{8}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{8}{3} y (- \frac{3}{8}) < \frac{4}{3} (- \frac{3}{8})$

Simplify the left side.

Combine $y$ and $\frac{8}{3}$ .

$- \frac{y \cdot 8}{3} (- \frac{3}{8}) < \frac{4}{3} (- \frac{3}{8})$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{y \cdot 8}{3}$ into the numerator.

$\frac{- y \cdot 8}{3} (- \frac{3}{8}) < \frac{4}{3} (- \frac{3}{8})$

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$\frac{- y \cdot 8}{3} \cdot \frac{- 3}{8} < \frac{4}{3} (- \frac{3}{8})$

Factor $8$ out of $- y \cdot 8$ .

$\frac{8 \cdot (- y)}{3} \cdot \frac{- 3}{8} < \frac{4}{3} (- \frac{3}{8})$

Cancel the common factor.

$\frac{8 \cdot (- y)}{3} \cdot \frac{- 3}{8} < \frac{4}{3} (- \frac{3}{8})$

Rewrite the expression.

$\frac{- y}{3} \cdot - 3 < \frac{4}{3} (- \frac{3}{8})$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$\frac{- y}{3} \cdot (3 (- 1)) < \frac{4}{3} (- \frac{3}{8})$

Cancel the common factor.

$\frac{- y}{3} \cdot (3 \cdot - 1) < \frac{4}{3} (- \frac{3}{8})$

Rewrite the expression.

$- y \cdot - 1 < \frac{4}{3} (- \frac{3}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y < \frac{4}{3} (- \frac{3}{8})$

Multiply $y$ by $1$ .

$y < \frac{4}{3} (- \frac{3}{8})$

Simplify the right side.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$y < \frac{4}{3} \cdot \frac{- 3}{8}$

Factor $4$ out of $8$ .

$y < \frac{4}{3} \cdot \frac{- 3}{4 (2)}$

Cancel the common factor.

$y < \frac{4}{3} \cdot \frac{- 3}{4 \cdot 2}$

Rewrite the expression.

$y < \frac{1}{3} \cdot \frac{- 3}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$y < \frac{1}{3} \cdot \frac{3 (- 1)}{2}$

Cancel the common factor.

$y < \frac{1}{3} \cdot \frac{3 \cdot - 1}{2}$

Rewrite the expression.

$y < \frac{- 1}{2}$

Move the negative in front of the fraction.

$y < - \frac{1}{2}$

The result can be shown in multiple forms.

Inequality Form:

$y < - \frac{1}{2}$

Interval Notation:

$(- \infty, - \frac{1}{2})$

Solve the Inequality for y 4/3<-8/3y

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