Solve m+1/3<5m-1/6+1

$$\frac { m + 1 } { 3 } < \frac { 5 m - 1 } { 6 } + 1$$

Solve for m

$$m>-1$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,6. Since 6 is positive, the inequality direction remains the same.

$$2\left(m+1\right)<5m-1+6$$

Use the distributive property to multiply 2 by m+1.

$$2m+2<5m-1+6$$

Add -1 and 6 to get 5.

$$2m+2<5m+5$$

Subtract 5m from both sides.

$$2m+2-5m<5$$

Combine 2m and -5m to get -3m.

$$-3m+2<5$$

Subtract 2 from both sides.

$$-3m<5-2$$

Subtract 2 from 5 to get 3.

$$-3m<3$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$m>\frac{3}{-3}$$

Divide 3 by -3 to get -1.

$$m>-1$$