Solve 3b+1/2>b+2

$$3 b + \frac { 1 } { 2 } > b + 2$$

Solve for b

$$b>\frac{3}{4}$$

Solution Steps

Subtract b from both sides.

$$3b+\frac{1}{2}-b>2$$

Combine 3b and -b to get 2b.

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

Subtract \frac{1}{2} from both sides.

$$2b>2-\frac{1}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$2b>\frac{4}{2}-\frac{1}{2}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$2b>\frac{4-1}{2}$$

Subtract 1 from 4 to get 3.

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

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

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

Express \frac{\frac{3}{2}}{2} as a single fraction.

$$b>\frac{3}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$b>\frac{3}{4}$$