Solve 2x-1/2-1<5x+2/3

$$\frac{ 2x-1 }{ 2 } -1 < \frac{ 5x+2 }{ 3 }$$

Solve for x

$$x>-\frac{13}{4}$$

Solution Steps

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

$$3\left(2x-1\right)-6<2\left(5x+2\right)$$

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

$$6x-3-6<2\left(5x+2\right)$$

Subtract 6 from -3 to get -9.

$$6x-9<2\left(5x+2\right)$$

Use the distributive property to multiply 2 by 5x+2.

$$6x-9<10x+4$$

Subtract 10x from both sides.

$$6x-9-10x<4$$

Combine 6x and -10x to get -4x.

$$-4x-9<4$$

Add 9 to both sides.

$$-4x<4+9$$

Add 4 and 9 to get 13.

$$-4x<13$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x>-\frac{13}{4}$$