Solve for x -9/4x<-72

$- \frac{9}{4} x < - 72$

Step 1

Multiply each term in $- \frac{9}{4} x < - 72$ by $- \frac{4}{9}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{9}{4} x (- \frac{4}{9}) > - 72 (- \frac{4}{9})$

Step 2

Simplify the left side.

Combine $x$ and $\frac{9}{4}$ .

$- \frac{x \cdot 9}{4} (- \frac{4}{9}) > - 72 (- \frac{4}{9})$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{x \cdot 9}{4}$ into the numerator.

$\frac{- x \cdot 9}{4} (- \frac{4}{9}) > - 72 (- \frac{4}{9})$

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$\frac{- x \cdot 9}{4} \cdot \frac{- 4}{9} > - 72 (- \frac{4}{9})$

Factor $9$ out of $- x \cdot 9$ .

$\frac{9 \cdot (- x)}{4} \cdot \frac{- 4}{9} > - 72 (- \frac{4}{9})$

Cancel the common factor.

$\frac{9 \cdot (- x)}{4} \cdot \frac{- 4}{9} > - 72 (- \frac{4}{9})$

Rewrite the expression.

$\frac{- x}{4} \cdot - 4 > - 72 (- \frac{4}{9})$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$\frac{- x}{4} \cdot (4 (- 1)) > - 72 (- \frac{4}{9})$

Cancel the common factor.

$\frac{- x}{4} \cdot (4 \cdot - 1) > - 72 (- \frac{4}{9})$

Rewrite the expression.

$- x \cdot - 1 > - 72 (- \frac{4}{9})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x > - 72 (- \frac{4}{9})$

Multiply $x$ by $1$ .

$x > - 72 (- \frac{4}{9})$

Step 3

Simplify the right side.

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{4}{9}$ into the numerator.

$x > - 72 (\frac{- 4}{9})$

Factor $9$ out of $- 72$ .

$x > 9 (- 8) \frac{- 4}{9}$

Cancel the common factor.

$x > 9 \cdot - 8 \frac{- 4}{9}$

Rewrite the expression.

$x > - 8 \cdot - 4$

Multiply $- 8$ by $- 4$ .

$x > 32$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 32$

Interval Notation:

$(32, \infty)$

Solve for x -9/4x<-72

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