Solve x+6/7>-1/4

$$\frac{ x+6 }{ 7 } > \frac{ -1 }{ 4 }$$

Solve for x

$$x>-\frac{31}{4}$$

Solution Steps

Multiply both sides of the equation by 28, the least common multiple of 7,4. Since 28 is positive, the inequality direction remains the same.

$$4\left(x+6\right)>7\left(-1\right)$$

Use the distributive property to multiply 4 by x+6.

$$4x+24>7\left(-1\right)$$

Multiply 7 and -1 to get -7.

$$4x+24>-7$$

Subtract 24 from both sides.

$$4x>-7-24$$

Subtract 24 from -7 to get -31.

$$4x>-31$$

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

$$x>-\frac{31}{4}$$