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

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

Solve for x

$$x<38$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)-24<3\left(x+4\right)$$

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

$$4x-2-24<3\left(x+4\right)$$

Subtract 24 from -2 to get -26.

$$4x-26<3\left(x+4\right)$$

Use the distributive property to multiply 3 by x+4.

$$4x-26<3x+12$$

Subtract 3x from both sides.

$$4x-26-3x<12$$

Combine 4x and -3x to get x.

$$x-26<12$$

Add 26 to both sides.

$$x<12+26$$

Add 12 and 26 to get 38.

$$x<38$$