Pre-Algebra Examples

$- 12 x - 2 y \geq - 42$

Step 1

Add $12 x$ to both sides of the inequality.

$- 2 y \geq - 42 + 12 x$

Step 2

Divide each term in $- 2 y \geq - 42 + 12 x$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 y \geq - 42 + 12 x$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} \leq \frac{- 42}{- 2} + \frac{12 x}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} \leq \frac{- 42}{- 2} + \frac{12 x}{- 2}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{- 42}{- 2} + \frac{12 x}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $- 42$ by $- 2$ .

$y \leq 21 + \frac{12 x}{- 2}$

Step 2.3.1.2

Cancel the common factor of $12$ and $- 2$ .

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Step 2.3.1.2.1

Factor $2$ out of $12 x$ .

$y \leq 21 + \frac{2 (6 x)}{- 2}$

Step 2.3.1.2.2

Move the negative one from the denominator of $\frac{6 x}{- 1}$ .

$y \leq 21 - 1 \cdot (6 x)$

Step 2.3.1.3

Rewrite $- 1 \cdot (6 x)$ as $- (6 x)$ .

$y \leq 21 - (6 x)$

Step 2.3.1.4

Multiply $6$ by $- 1$ .

$y \leq 21 - 6 x$