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

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

Solve for x

$$x>\frac{5}{2}$$

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.

$$4x+3>2\left(4+x\right)$$

Use the distributive property to multiply 2 by 4+x.

$$4x+3>8+2x$$

Subtract 2x from both sides.

$$4x+3-2x>8$$

Combine 4x and -2x to get 2x.

$$2x+3>8$$

Subtract 3 from both sides.

$$2x>8-3$$

Subtract 3 from 8 to get 5.

$$2x>5$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x>\frac{5}{2}$$