Solve =3x+5/5-2x+3/2>x-8/3

$$= \frac { 3 x + 5 } { 5 } - \frac { 2 x + 3 } { 2 } > \frac { x - 8 } { 3 }$$

Solve for x

$$x<\frac{65}{22}$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,2,3. Since 30 is positive, the inequality direction remains the same.

$$6\left(3x+5\right)-15\left(2x+3\right)>10\left(x-8\right)$$

Use the distributive property to multiply 6 by 3x+5.

$$18x+30-15\left(2x+3\right)>10\left(x-8\right)$$

Use the distributive property to multiply -15 by 2x+3.

$$18x+30-30x-45>10\left(x-8\right)$$

Combine 18x and -30x to get -12x.

$$-12x+30-45>10\left(x-8\right)$$

Subtract 45 from 30 to get -15.

$$-12x-15>10\left(x-8\right)$$

Use the distributive property to multiply 10 by x-8.

$$-12x-15>10x-80$$

Subtract 10x from both sides.

$$-12x-15-10x>-80$$

Combine -12x and -10x to get -22x.

$$-22x-15>-80$$

Add 15 to both sides.

$$-22x>-80+15$$

Add -80 and 15 to get -65.

$$-22x>-65$$

Divide both sides by -22. Since -22 is negative, the inequality direction is changed.

$$x<\frac{-65}{-22}$$

Fraction \frac{-65}{-22} can be simplified to \frac{65}{22} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{65}{22}$$