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

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

Solve for x

$$x<-\frac{5}{18}$$

Solution Steps

Add 2x to both sides.

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

Combine \frac{2}{5}x and 2x to get \frac{12}{5}x.

$$\frac{12}{5}x+1<\frac{1}{3}$$

Subtract 1 from both sides.

$$\frac{12}{5}x<\frac{1}{3}-1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{12}{5}x<\frac{1}{3}-\frac{3}{3}$$

Since \frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{5}x<\frac{1-3}{3}$$

Subtract 3 from 1 to get -2.

$$\frac{12}{5}x<-\frac{2}{3}$$

Multiply both sides by \frac{5}{12}, the reciprocal of \frac{12}{5}. Since \frac{12}{5} is positive, the inequality direction remains the same.

$$x<-\frac{2}{3}\times \frac{5}{12}$$

Multiply -\frac{2}{3} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{-2\times 5}{3\times 12}$$

Do the multiplications in the fraction \frac{-2\times 5}{3\times 12}.

$$x<\frac{-10}{36}$$

Reduce the fraction \frac{-10}{36} to lowest terms by extracting and canceling out 2.

$$x<-\frac{5}{18}$$