Pre-Algebra Examples

$\frac{x}{- 4} \leq 2$

Step 1

Multiply both sides by $- 4$ .

$\frac{x}{- 4} \cdot - 4 \geq 2 \cdot - 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{x}{- 4} \cdot - 4$ .

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Step 2.1.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1.1

Factor $4$ out of $- 4$ .

$\frac{x}{4 (- 1)} \cdot - 4 \geq 2 \cdot - 4$

Step 2.1.1.1.2

Factor $4$ out of $- 4$ .

$\frac{x}{4 \cdot - 1} \cdot (4 \cdot - 1) \geq 2 \cdot - 4$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{x}{4 \cdot - 1} \cdot (4 \cdot - 1) \geq 2 \cdot - 4$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{x}{- 1} \cdot - 1 \geq 2 \cdot - 4$

Step 2.1.1.2

Combine $\frac{x}{- 1}$ and $- 1$ .

$\frac{x \cdot - 1}{- 1} \geq 2 \cdot - 4$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{x \cdot - 1}{- 1}$ .

$- 1 \cdot (x \cdot - 1) \geq 2 \cdot - 4$

Step 2.1.1.3.2

Rewrite $- 1 \cdot (x \cdot - 1)$ as $- (x \cdot - 1)$ .

$- (x \cdot - 1) \geq 2 \cdot - 4$

Step 2.1.1.3.3

Move $- 1$ to the left of $x$ .

$- (- 1 \cdot x) \geq 2 \cdot - 4$

Step 2.1.1.3.4

Rewrite $- 1 x$ as $- x$ .

$- - x \geq 2 \cdot - 4$

Step 2.1.1.4

Multiply $- - x$ .

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 x \geq 2 \cdot - 4$

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$x \geq 2 \cdot - 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $- 4$ .

$x \geq - 8$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 8$

Interval Notation:

$[- 8, \infty)$