Algebra Examples

$- 4 \leq 5 - \frac{4}{5} x < 6$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $x$ and $\frac{4}{5}$ .

$- 4 \leq 5 - \frac{x \cdot 4}{5} < 6$

Step 1.2

Move $4$ to the left of $x$ .

$- 4 \leq 5 - \frac{4 x}{5} < 6$

Step 2

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

Tap for more steps...

Step 2.1

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

$- 4 - 5 \leq - \frac{4 x}{5} < 6 - 5$

Step 2.2

Subtract $5$ from $- 4$ .

$- 9 \leq - \frac{4 x}{5} < 6 - 5$

Step 2.3

Multiply each term in the inequality by $5$ .

$- 9 \cdot 5 \leq - \frac{4 x}{5} \cdot 5 < 6 \cdot 5 - 5 \cdot 5$

Step 2.4

Multiply $- 9$ by $5$ .

$- 45 \leq - \frac{4 x}{5} \cdot 5 < 6 \cdot 5 - 5 \cdot 5$

Step 2.5

Cancel the common factor of $5$ .

Tap for more steps...

Step 2.5.1

Move the leading negative in $- \frac{4 x}{5}$ into the numerator.

$- 45 \leq \frac{- 4 x}{5} \cdot 5 < 6 \cdot 5 - 5 \cdot 5$

Step 2.5.2

Cancel the common factor.

$- 45 \leq \frac{- 4 x}{5} \cdot 5 < 6 \cdot 5 - 5 \cdot 5$

Step 2.5.3

Rewrite the expression.

$- 45 \leq - 4 x < 6 \cdot 5 - 5 \cdot 5$

Step 2.6

Simplify each term.

Tap for more steps...

Step 2.6.1

Multiply $6$ by $5$ .

$- 45 \leq - 4 x < 30 - 5 \cdot 5$

Step 2.6.2

Multiply $- 5$ by $5$ .

$- 45 \leq - 4 x < 30 - 25$

Step 2.7

Subtract $25$ from $30$ .

$- 45 \leq - 4 x < 5$

Step 3

Divide each term in the inequality by $- 4$ .

$\frac{- 45}{- 4} \geq \frac{- 4 x}{- 4} > \frac{5}{- 4}$

Step 4

Dividing two negative values results in a positive value.

$\frac{45}{4} \geq \frac{- 4 x}{- 4} > \frac{5}{- 4}$

Step 5

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\frac{45}{4} \geq \frac{- 4 x}{- 4} > \frac{5}{- 4}$

Step 5.2

Divide $x$ by $1$ .

$\frac{45}{4} \geq x > \frac{5}{- 4}$

Step 6

Move the negative in front of the fraction.

$\frac{45}{4} \geq x > - \frac{5}{4}$

Step 7

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

$- \frac{5}{4} < x \leq \frac{45}{4}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$- \frac{5}{4} < x \leq \frac{45}{4}$

Interval Notation:

$(- \frac{5}{4}, \frac{45}{4}]$

Step 9