Solve 2x+5/2+3x>x-3/3

$$\frac { 2 x + 5 } { 2 } + 3 x > \frac { x - 3 } { 3 }$$

Solve for x

$$x>-\frac{21}{22}$$

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.

$$3\left(2x+5\right)+18x>2\left(x-3\right)$$

Use the distributive property to multiply 3 by 2x+5.

$$6x+15+18x>2\left(x-3\right)$$

Combine 6x and 18x to get 24x.

$$24x+15>2\left(x-3\right)$$

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

$$24x+15>2x-6$$

Subtract 2x from both sides.

$$24x+15-2x>-6$$

Combine 24x and -2x to get 22x.

$$22x+15>-6$$

Subtract 15 from both sides.

$$22x>-6-15$$

Subtract 15 from -6 to get -21.

$$22x>-21$$

Divide both sides by 22. Since 22 is positive, the inequality direction remains the same.

$$x>-\frac{21}{22}$$