Algebra Examples

$\frac{7}{2} \geq b + \frac{9}{5}$

Step 1

Rewrite so $b$ is on the left side of the inequality.

$b + \frac{9}{5} \leq \frac{7}{2}$

Step 2

Move all terms not containing $b$ to the right side of the inequality.

Tap for more steps...

Step 2.1

Subtract $\frac{9}{5}$ from both sides of the inequality.

$b \leq \frac{7}{2} - \frac{9}{5}$

Step 2.2

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b \leq \frac{7}{2} \cdot \frac{5}{5} - \frac{9}{5}$

Step 2.3

To write $- \frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b \leq \frac{7}{2} \cdot \frac{5}{5} - \frac{9}{5} \cdot \frac{2}{2}$

Step 2.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.4.1

Multiply $\frac{7}{2}$ by $\frac{5}{5}$ .

$b \leq \frac{7 \cdot 5}{2 \cdot 5} - \frac{9}{5} \cdot \frac{2}{2}$

Step 2.4.2

Multiply $2$ by $5$ .

$b \leq \frac{7 \cdot 5}{10} - \frac{9}{5} \cdot \frac{2}{2}$

Step 2.4.3

Multiply $\frac{9}{5}$ by $\frac{2}{2}$ .

$b \leq \frac{7 \cdot 5}{10} - \frac{9 \cdot 2}{5 \cdot 2}$

Step 2.4.4

Multiply $5$ by $2$ .

$b \leq \frac{7 \cdot 5}{10} - \frac{9 \cdot 2}{10}$

Step 2.5

Combine the numerators over the common denominator.

$b \leq \frac{7 \cdot 5 - 9 \cdot 2}{10}$

Step 2.6

Simplify the numerator.

Tap for more steps...

Step 2.6.1

Multiply $7$ by $5$ .

$b \leq \frac{35 - 9 \cdot 2}{10}$

Step 2.6.2

Multiply $- 9$ by $2$ .

$b \leq \frac{35 - 18}{10}$

Step 2.6.3

Subtract $18$ from $35$ .

$b \leq \frac{17}{10}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$b \leq \frac{17}{10}$

Interval Notation:

$(- \infty, \frac{17}{10}]$