Solve 5-x/3<3x/2-4

$$5- \frac{ x }{ 3 } < \frac{ 3x }{ 2 } -4$$

Solve for x

$$x>\frac{54}{11}$$

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.

$$30-2x<3\times 3x-24$$

Multiply 3 and 3 to get 9.

$$30-2x<9x-24$$

Subtract 9x from both sides.

$$30-2x-9x<-24$$

Combine -2x and -9x to get -11x.

$$30-11x<-24$$

Subtract 30 from both sides.

$$-11x<-24-30$$

Subtract 30 from -24 to get -54.

$$-11x<-54$$

Divide both sides by -11. Since -11 is negative, the inequality direction is changed.

$$x>\frac{-54}{-11}$$

Fraction \frac{-54}{-11} can be simplified to \frac{54}{11} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{54}{11}$$