Algebra Examples

$- \frac{5 x}{6} \geq 22$

Step 1

Divide each term in $- \frac{5 x}{6} \geq 22$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- \frac{5 x}{6} \geq 22$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{5 x}{6}}{- 1} \leq \frac{22}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{5 x}{6}}{1} \leq \frac{22}{- 1}$

Step 1.2.2

Divide $\frac{5 x}{6}$ by $1$ .

$\frac{5 x}{6} \leq \frac{22}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $22$ by $- 1$ .

$\frac{5 x}{6} \leq - 22$

Step 2

Multiply both sides by $6$ .

$\frac{5 x}{6} \cdot 6 \leq - 22 \cdot 6$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $6$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{5 x}{6} \cdot 6 \leq - 22 \cdot 6$

Step 3.1.1.2

Rewrite the expression.

$5 x \leq - 22 \cdot 6$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 22$ by $6$ .

$5 x \leq - 132$

Step 4

Divide each term in $5 x \leq - 132$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x \leq - 132$ by $5$ .

$\frac{5 x}{5} \leq \frac{- 132}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{- 132}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 132}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x \leq - \frac{132}{5}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{132}{5}$

Interval Notation:

$(- \infty, - \frac{132}{5}]$