Algebra Examples

$10 > \frac{5 u}{4} > \frac{15}{2}$

Step 1

Multiply each term in the inequality by $4$ .

$10 \cdot 4 > \frac{5 u}{4} \cdot 4 > \frac{15}{2} \cdot 4$

Step 2

Multiply $10$ by $4$ .

$40 > \frac{5 u}{4} \cdot 4 > \frac{15}{2} \cdot 4$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$40 > \frac{5 u}{4} \cdot 4 > \frac{15}{2} \cdot 4$

Step 3.2

Rewrite the expression.

$40 > 5 u > \frac{15}{2} \cdot 4$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $4$ .

$40 > 5 u > \frac{15}{2} \cdot (2 (2))$

Step 4.2

Cancel the common factor.

$40 > 5 u > \frac{15}{2} \cdot (2 \cdot 2)$

Step 4.3

Rewrite the expression.

$40 > 5 u > 15 \cdot 2$

Step 5

Multiply $15$ by $2$ .

$40 > 5 u > 30$

Step 6

Divide each term in the inequality by $5$ .

$\frac{40}{5} > \frac{5 u}{5} > \frac{30}{5}$

Step 7

Divide $40$ by $5$ .

$8 > \frac{5 u}{5} > \frac{30}{5}$

Step 8

Cancel the common factor of $5$ .

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Step 8.1

Cancel the common factor.

$8 > \frac{5 u}{5} > \frac{30}{5}$

Step 8.2

Divide $u$ by $1$ .

$8 > u > \frac{30}{5}$

Step 9

Divide $30$ by $5$ .

$8 > u > 6$

Step 10

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

$6 < u < 8$

Step 11

The result can be shown in multiple forms.

Inequality Form:

$6 < u < 8$

Interval Notation:

$(6, 8)$

Step 12