Algebra Examples

$0.4 \leq \frac{0.02 - 0.01 x}{0.2} < 0.8$

Step 1

Factor $0.01$ out of $0.02 - 0.01 x$ .

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Step 1.1

Factor $0.01$ out of $0.02$ .

$0.4 \leq \frac{0.01 (2) - 0.01 x}{0.2} < 0.8$

Step 1.2

Factor $0.01$ out of $- 0.01 x$ .

$0.4 \leq \frac{0.01 (2) + 0.01 (- x)}{0.2} < 0.8$

Step 1.3

Factor $0.01$ out of $0.01 (2) + 0.01 (- x)$ .

$0.4 \leq \frac{0.01 (2 - x)}{0.2} < 0.8$

Step 2

Factor $0.2$ out of $0.2$ .

$0.4 \leq \frac{0.01 (2 - x)}{0.2 (1)} < 0.8$

Step 3

Separate fractions.

$0.4 \leq \frac{0.01}{0.2} \cdot \frac{2 - x}{1} < 0.8$

Step 4

Divide $0.01$ by $0.2$ .

$0.4 \leq 0.05 (\frac{2 - x}{1}) < 0.8$

Step 5

Cancel the common factor of $0.05$ .

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Step 5.1

Factor $0.05$ out of $1$ .

$0.4 \leq 0.05 (\frac{2 - x}{0.05 \cdot 20}) < 0.8$

Step 5.2

Cancel the common factor.

$0.4 \leq 0.05 (\frac{2 - x}{0.05 \cdot 20}) < 0.8$

Step 5.3

Rewrite the expression.

$0.4 \leq \frac{2 - x}{20} < 0.8$

Step 6

Multiply each term in the inequality by $20$ .

$0.4 \cdot 20 \leq \frac{2 - x}{20} \cdot 20 < 0.8 \cdot 20$

Step 7

Multiply $0.4$ by $20$ .

$8 \leq \frac{2 - x}{20} \cdot 20 < 0.8 \cdot 20$

Step 8

Cancel the common factor of $20$ .

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Step 8.1

Cancel the common factor.

$8 \leq \frac{2 - x}{20} \cdot 20 < 0.8 \cdot 20$

Step 8.2

Rewrite the expression.

$8 \leq 2 - x < 0.8 \cdot 20$

Step 9

Multiply $0.8$ by $20$ .

$8 \leq 2 - x < 16$

Step 10

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

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Step 10.1

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$8 - 2 \leq - x < 16 - 2$

Step 10.2

Subtract $2$ from $8$ .

$6 \leq - x < 16 - 2$

Step 10.3

Subtract $2$ from $16$ .

$6 \leq - x < 14$

Step 11

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

$\frac{6}{- 1} \geq \frac{- x}{- 1} > \frac{14}{- 1}$

Step 12

Divide $6$ by $- 1$ .

$- 6 \geq \frac{- x}{- 1} > \frac{14}{- 1}$

Step 13

Dividing two negative values results in a positive value.

$- 6 \geq \frac{x}{1} > \frac{14}{- 1}$

Step 14

Divide $x$ by $1$ .

$- 6 \geq x > \frac{14}{- 1}$

Step 15

Divide $14$ by $- 1$ .

$- 6 \geq x > - 14$

Step 16

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 14 < x \leq - 6$

Step 17

The result can be shown in multiple forms.

Inequality Form:

$- 14 < x \leq - 6$

Interval Notation:

$(- 14, - 6]$

Step 18