Pre-Algebra Examples

$1 \frac{1}{2} + b > 7$

Step 1

Simplify the left side.

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Step 1.1

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$1 + \frac{1}{2} + b > 7$

Step 1.1.2

Add $1$ and $\frac{1}{2}$ .

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Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{2}{2} + \frac{1}{2} + b > 7$

Step 1.1.2.2

Combine the numerators over the common denominator.

$\frac{2 + 1}{2} + b > 7$

Step 1.1.2.3

Add $2$ and $1$ .

$\frac{3}{2} + b > 7$

Step 2

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

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Step 2.1

Subtract $\frac{3}{2}$ from both sides of the inequality.

$b > 7 - \frac{3}{2}$

Step 2.2

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

$b > 7 \cdot \frac{2}{2} - \frac{3}{2}$

Step 2.3

Combine $7$ and $\frac{2}{2}$ .

$b > \frac{7 \cdot 2}{2} - \frac{3}{2}$

Step 2.4

Combine the numerators over the common denominator.

$b > \frac{7 \cdot 2 - 3}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $2$ .

$b > \frac{14 - 3}{2}$

Step 2.5.2

Subtract $3$ from $14$ .

$b > \frac{11}{2}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$b > \frac{11}{2}$

Interval Notation:

$(\frac{11}{2}, \infty)$