Solve x+4/3>2x-1/4

$$x+ \frac{ 4 }{ 3 } > \frac{ 2x-1 }{ 4 }$$

Solve for x

$$x>-\frac{19}{6}$$

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.

$$12x+16>3\left(2x-1\right)$$

Use the distributive property to multiply 3 by 2x-1.

$$12x+16>6x-3$$

Subtract 6x from both sides.

$$12x+16-6x>-3$$

Combine 12x and -6x to get 6x.

$$6x+16>-3$$

Subtract 16 from both sides.

$$6x>-3-16$$

Subtract 16 from -3 to get -19.

$$6x>-19$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$x>-\frac{19}{6}$$