Solve h+1/3+h-2/4geq1

$$\frac { h + 1 } { 3 } + \frac { h - 2 } { 4 } \geq 1$$

Solve for h

$$h\geq 2$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 3,4. Since 12 is positive, the inequality direction remains the same.

$$4\left(h+1\right)+3\left(h-2\right)\geq 12$$

Use the distributive property to multiply 4 by h+1.

$$4h+4+3\left(h-2\right)\geq 12$$

Use the distributive property to multiply 3 by h-2.

$$4h+4+3h-6\geq 12$$

Combine 4h and 3h to get 7h.

$$7h+4-6\geq 12$$

Subtract 6 from 4 to get -2.

$$7h-2\geq 12$$

Add 2 to both sides.

$$7h\geq 12+2$$

Add 12 and 2 to get 14.

$$7h\geq 14$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$h\geq \frac{14}{7}$$

Divide 14 by 7 to get 2.

$$h\geq 2$$