Solve 5m+4/6geq7/8+1-m/3

$$\frac{ 5m+4 }{ 6 } \geq \frac{ 7 }{ 8 } + \frac{ 1-m }{ 3 }$$

Solve for m

$$m\geq \frac{13}{28}$$

Solution Steps

Multiply both sides of the equation by 24, the least common multiple of 6,8,3. Since 24 is positive, the inequality direction remains the same.

$$4\left(5m+4\right)\geq 21+8\left(1-m\right)$$

Use the distributive property to multiply 4 by 5m+4.

$$20m+16\geq 21+8\left(1-m\right)$$

Use the distributive property to multiply 8 by 1-m.

$$20m+16\geq 21+8-8m$$

Add 21 and 8 to get 29.

$$20m+16\geq 29-8m$$

Add 8m to both sides.

$$20m+16+8m\geq 29$$

Combine 20m and 8m to get 28m.

$$28m+16\geq 29$$

Subtract 16 from both sides.

$$28m\geq 29-16$$

Subtract 16 from 29 to get 13.

$$28m\geq 13$$

Divide both sides by 28. Since 28 is positive, the inequality direction remains the same.

$$m\geq \frac{13}{28}$$