Solve 2b-5/8+3leqb+6/12

$$\frac { 2 b - 5 } { 8 } + 3 \leq \frac { b + 6 } { 12 }$$

Solve for b

$$b\leq -\frac{45}{4}$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 8,12. Since 24 is positive, the inequality direction remains the same.

$$3\left(2b-5\right)+72\leq 2\left(b+6\right)$$

Use the distributive property to multiply 3 by 2b-5.

$$6b-15+72\leq 2\left(b+6\right)$$

Add -15 and 72 to get 57.

$$6b+57\leq 2\left(b+6\right)$$

Use the distributive property to multiply 2 by b+6.

$$6b+57\leq 2b+12$$

Subtract 2b from both sides.

$$6b+57-2b\leq 12$$

Combine 6b and -2b to get 4b.

$$4b+57\leq 12$$

Subtract 57 from both sides.

$$4b\leq 12-57$$

Subtract 57 from 12 to get -45.

$$4b\leq -45$$

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

$$b\leq -\frac{45}{4}$$