Algebra Examples

$- \frac{5}{3} x \leq - 5$

Step 1

Multiply each term in $- \frac{5}{3} x \leq - 5$ by $- \frac{3}{5}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{5}{3} x (- \frac{3}{5}) \geq - 5 (- \frac{3}{5})$

Step 2

Simplify the left side.

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Step 2.1

Combine $x$ and $\frac{5}{3}$ .

$- \frac{x \cdot 5}{3} (- \frac{3}{5}) \geq - 5 (- \frac{3}{5})$

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Move the leading negative in $- \frac{x \cdot 5}{3}$ into the numerator.

$\frac{- x \cdot 5}{3} (- \frac{3}{5}) \geq - 5 (- \frac{3}{5})$

Step 2.2.2

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{- x \cdot 5}{3} \cdot \frac{- 3}{5} \geq - 5 (- \frac{3}{5})$

Step 2.2.3

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

$\frac{5 \cdot (- x)}{3} \cdot \frac{- 3}{5} \geq - 5 (- \frac{3}{5})$

Step 2.2.4

Cancel the common factor.

$\frac{5 \cdot (- x)}{3} \cdot \frac{- 3}{5} \geq - 5 (- \frac{3}{5})$

Step 2.2.5

Rewrite the expression.

$\frac{- x}{3} \cdot - 3 \geq - 5 (- \frac{3}{5})$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $- 3$ .

$\frac{- x}{3} \cdot (3 (- 1)) \geq - 5 (- \frac{3}{5})$

Step 2.3.2

Cancel the common factor.

$\frac{- x}{3} \cdot (3 \cdot - 1) \geq - 5 (- \frac{3}{5})$

Step 2.3.3

Rewrite the expression.

$- x \cdot - 1 \geq - 5 (- \frac{3}{5})$

Step 2.4

Multiply.

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Step 2.4.1

Multiply $- 1$ by $- 1$ .

$1 x \geq - 5 (- \frac{3}{5})$

Step 2.4.2

Multiply $x$ by $1$ .

$x \geq - 5 (- \frac{3}{5})$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $5$ .

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Step 3.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$x \geq - 5 (\frac{- 3}{5})$

Step 3.1.2

Factor $5$ out of $- 5$ .

$x \geq 5 (- 1) \frac{- 3}{5}$

Step 3.1.3

Cancel the common factor.

$x \geq 5 \cdot - 1 \frac{- 3}{5}$

Step 3.1.4

Rewrite the expression.

$x \geq - - 3$

Step 3.2

Multiply $- 1$ by $- 3$ .

$x \geq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 3$

Interval Notation:

$[3, \infty)$