Solve -4b-(3/4+(-5b)+11/4)<1/2

$$- 4 b - ( \frac { 3 } { 4 } + ( - 5 b ) + 1 \frac { 1 } { 4 } ) < \frac { 1 } { 2 }$$

Solve for b

$$b<\frac{5}{2}$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 4,2. Since 4 is positive, the inequality direction remains the same.

$$-16b-4\left(\frac{3}{4}-5b+\frac{1\times 4+1}{4}\right)<2$$

Multiply 1 and 4 to get 4.

$$-16b-4\left(\frac{3}{4}-5b+\frac{4+1}{4}\right)<2$$

Add 4 and 1 to get 5.

$$-16b-4\left(\frac{3}{4}-5b+\frac{5}{4}\right)<2$$

Since \frac{3}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$-16b-4\left(\frac{3+5}{4}-5b\right)<2$$

Add 3 and 5 to get 8.

$$-16b-4\left(\frac{8}{4}-5b\right)<2$$

Divide 8 by 4 to get 2.

$$-16b-4\left(2-5b\right)<2$$

Use the distributive property to multiply -4 by 2-5b.

$$-16b-8+20b<2$$

Combine -16b and 20b to get 4b.

$$4b-8<2$$

Add 8 to both sides.

$$4b<2+8$$

Add 2 and 8 to get 10.

$$4b<10$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$b<\frac{10}{4}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$b<\frac{5}{2}$$