Solve x/4-1<2x+1/2

$$\frac{ x }{ 4 } -1 < 2x+ \frac{ 1 }{ 2 }$$

Solve for x

$$x>-\frac{6}{7}$$

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 4,2. Since 4 is positive, the inequality direction remains the same.

$$x-4<8x+2$$

Subtract 8x from both sides.

$$x-4-8x<2$$

Combine x and -8x to get -7x.

$$-7x-4<2$$

Add 4 to both sides.

$$-7x<2+4$$

Add 2 and 4 to get 6.

$$-7x<6$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x>-\frac{6}{7}$$