Solve the Inequality for t -5/9t<25

$- \frac{5}{9} t < 25$

Multiply each term in $- \frac{5}{9} t < 25$ by $- \frac{9}{5}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{5}{9} t (- \frac{9}{5}) > 25 (- \frac{9}{5})$

Simplify the left side.

Combine $t$ and $\frac{5}{9}$ .

$- \frac{t \cdot 5}{9} (- \frac{9}{5}) > 25 (- \frac{9}{5})$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{t \cdot 5}{9}$ into the numerator.

$\frac{- t \cdot 5}{9} (- \frac{9}{5}) > 25 (- \frac{9}{5})$

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$\frac{- t \cdot 5}{9} \cdot \frac{- 9}{5} > 25 (- \frac{9}{5})$

Factor $5$ out of $- t \cdot 5$ .

$\frac{5 \cdot (- t)}{9} \cdot \frac{- 9}{5} > 25 (- \frac{9}{5})$

Cancel the common factor.

$\frac{5 \cdot (- t)}{9} \cdot \frac{- 9}{5} > 25 (- \frac{9}{5})$

Rewrite the expression.

$\frac{- t}{9} \cdot - 9 > 25 (- \frac{9}{5})$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9$ .

$\frac{- t}{9} \cdot (9 (- 1)) > 25 (- \frac{9}{5})$

Cancel the common factor.

$\frac{- t}{9} \cdot (9 \cdot - 1) > 25 (- \frac{9}{5})$

Rewrite the expression.

$- t \cdot - 1 > 25 (- \frac{9}{5})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 t > 25 (- \frac{9}{5})$

Multiply $t$ by $1$ .

$t > 25 (- \frac{9}{5})$

Simplify the right side.

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{9}{5}$ into the numerator.

$t > 25 (\frac{- 9}{5})$

Factor $5$ out of $25$ .

$t > 5 (5) \frac{- 9}{5}$

Cancel the common factor.

$t > 5 \cdot 5 \frac{- 9}{5}$

Rewrite the expression.

$t > 5 \cdot - 9$

Multiply $5$ by $- 9$ .

$t > - 45$

The result can be shown in multiple forms.

Inequality Form:

$t > - 45$

Interval Notation:

$(- 45, \infty)$

Solve the Inequality for t -5/9t<25

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