Algebra Examples

$- \frac{a x}{b} \geq c - d$

Step 1

Divide each term in $- \frac{a x}{b} \geq c - d$ by $- 1$ and simplify.

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Step 1.1

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

$\frac{- \frac{a x}{b}}{- 1} \leq \frac{c}{- 1} + \frac{- d}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{a x}{b}}{1} \leq \frac{c}{- 1} + \frac{- d}{- 1}$

Step 1.2.2

Divide $\frac{a x}{b}$ by $1$ .

$\frac{a x}{b} \leq \frac{c}{- 1} + \frac{- d}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

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

$\frac{a x}{b} \leq - 1 \cdot c + \frac{- d}{- 1}$

Step 1.3.1.2

Rewrite $- 1 \cdot c$ as $- c$ .

$\frac{a x}{b} \leq - c + \frac{- d}{- 1}$

Step 1.3.1.3

Dividing two negative values results in a positive value.

$\frac{a x}{b} \leq - c + \frac{d}{1}$

Step 1.3.1.4

Divide $d$ by $1$ .

$\frac{a x}{b} \leq - c + d$

Step 2

Multiply both sides by $b$ .

$\frac{a x}{b} b \leq (- c + d) b$

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 $b$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{a x}{b} b \leq (- c + d) b$

Step 3.1.1.2

Rewrite the expression.

$a x \leq (- c + d) b$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(- c + d) b$ .

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Step 3.2.1.1

Apply the distributive property.

$a x \leq - c b + d b$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Move $c$ .

$a x \leq - 1 b c + d b$

Step 3.2.1.2.2

Reorder $d$ and $b$ .

$a x \leq - 1 b c + b d$

Step 4

Divide each term in $a x \leq - 1 b c + b d$ by $a$ and simplify.

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Step 4.1

Divide each term in $a x \leq - 1 b c + b d$ by $a$ .

$\frac{a x}{a} \leq \frac{- 1 b c}{a} + \frac{b d}{a}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $a$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{a x}{a} \leq \frac{- 1 b c}{a} + \frac{b d}{a}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 1 b c}{a} + \frac{b d}{a}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$x \leq - \frac{b c}{a} + \frac{b d}{a}$