Solve 2/5(3-x)+2<-2

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

Solve for x

$$x>13$$

Solution Steps

Use the distributive property to multiply \frac{2}{5} by 3-x.

$$\frac{2}{5}\times 3+\frac{2}{5}\left(-1\right)x+2<-2$$

Express \frac{2}{5}\times 3 as a single fraction.

$$\frac{2\times 3}{5}+\frac{2}{5}\left(-1\right)x+2<-2$$

Multiply 2 and 3 to get 6.

$$\frac{6}{5}+\frac{2}{5}\left(-1\right)x+2<-2$$

Multiply \frac{2}{5} and -1 to get -\frac{2}{5}.

$$\frac{6}{5}-\frac{2}{5}x+2<-2$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{6}{5}-\frac{2}{5}x+\frac{10}{5}<-2$$

Since \frac{6}{5} and \frac{10}{5} have the same denominator, add them by adding their numerators.

$$\frac{6+10}{5}-\frac{2}{5}x<-2$$

Add 6 and 10 to get 16.

$$\frac{16}{5}-\frac{2}{5}x<-2$$

Subtract \frac{16}{5} from both sides.

$$-\frac{2}{5}x<-2-\frac{16}{5}$$

Convert -2 to fraction -\frac{10}{5}.

$$-\frac{2}{5}x<-\frac{10}{5}-\frac{16}{5}$$

Since -\frac{10}{5} and \frac{16}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{5}x<\frac{-10-16}{5}$$

Subtract 16 from -10 to get -26.

$$-\frac{2}{5}x<-\frac{26}{5}$$

Multiply both sides by -\frac{5}{2}, the reciprocal of -\frac{2}{5}. Since -\frac{2}{5} is negative, the inequality direction is changed.

$$x>-\frac{26}{5}\left(-\frac{5}{2}\right)$$

Multiply -\frac{26}{5} times -\frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-26\left(-5\right)}{5\times 2}$$

Do the multiplications in the fraction \frac{-26\left(-5\right)}{5\times 2}.

$$x>\frac{130}{10}$$

Divide 130 by 10 to get 13.

$$x>13$$