Solve 2(3-x)<-3.C

$$2 ( 3 - x ) < - 3 . C$$

Solve for x

$$x>\frac{9}{2}$$

Solution Steps

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

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

Subtract 3 from both sides.

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

Convert 3 to fraction \frac{6}{2}.

$$-x<-\frac{3}{2}-\frac{6}{2}$$

Since -\frac{3}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$-x<\frac{-3-6}{2}$$

Subtract 6 from -3 to get -9.

$$-x<-\frac{9}{2}$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-\frac{9}{2}}{-1}$$

Express \frac{-\frac{9}{2}}{-1} as a single fraction.

$$x>\frac{-9}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$x>\frac{-9}{-2}$$

Fraction \frac{-9}{-2} can be simplified to \frac{9}{2} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{9}{2}$$