Algebra Examples

$0 \geq \frac{5 - x}{4} \geq - 5$

Step 1

Solve $5 \leq x \leq 25$ .

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Step 1.1

Multiply each term in the inequality by $4$ .

$0 \cdot 4 \geq \frac{5 - x}{4} \cdot 4 \geq - 5 \cdot 4$

Step 1.2

Multiply $0$ by $4$ .

$0 \geq \frac{5 - x}{4} \cdot 4 \geq - 5 \cdot 4$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Cancel the common factor.

$0 \geq \frac{5 - x}{4} \cdot 4 \geq - 5 \cdot 4$

Step 1.3.2

Rewrite the expression.

$0 \geq 5 - x \geq - 5 \cdot 4$

Step 1.4

Multiply $- 5$ by $4$ .

$0 \geq 5 - x \geq - 20$

Step 1.5

Move all terms not containing $x$ from the center section of the inequality.

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Step 1.5.1

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$0 - 5 \geq - x \geq - 20 - 5$

Step 1.5.2

Subtract $5$ from $0$ .

$- 5 \geq - x \geq - 20 - 5$

Step 1.5.3

Subtract $5$ from $- 20$ .

$- 5 \geq - x \geq - 25$

Step 1.6

Multiply each term in the inequality by $- 1$ .

$\frac{- 5}{- 1} \leq \frac{- x}{- 1} \leq \frac{- 25}{- 1}$

Step 1.7

Divide $- 5$ by $- 1$ .

$5 \leq \frac{- x}{- 1} \leq \frac{- 25}{- 1}$

Step 1.8

Dividing two negative values results in a positive value.

$5 \leq \frac{x}{1} \leq \frac{- 25}{- 1}$

Step 1.9

Divide $x$ by $1$ .

$5 \leq x \leq \frac{- 25}{- 1}$

Step 1.10

Divide $- 25$ by $- 1$ .

$5 \leq x \leq 25$

Step 2

Use the inequality $5 \leq x \leq 25$ to build the set notation.

${x | 5 \leq x \leq 25}$

Step 3