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

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

Solve for x

$$x>\frac{5}{3}$$

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.

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

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

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

Subtract 6 from 15 to get 9.

$$3x+9<2\left(3x+2\right)$$

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

$$3x+9<6x+4$$

Subtract 6x from both sides.

$$3x+9-6x<4$$

Combine 3x and -6x to get -3x.

$$-3x+9<4$$

Subtract 9 from both sides.

$$-3x<4-9$$

Subtract 9 from 4 to get -5.

$$-3x<-5$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

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

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{5}{3}$$