Solve 4/3x+1<-2x-6/5

$$\frac { 4 } { 3 } x + 1 < - 2 x - \frac { 6 } { 5 }$$

Solve for x

$$x<-\frac{33}{50}$$

Solution Steps

Add 2x to both sides.

$$\frac{4}{3}x+1+2x<-\frac{6}{5}$$

Combine \frac{4}{3}x and 2x to get \frac{10}{3}x.

$$\frac{10}{3}x+1<-\frac{6}{5}$$

Subtract 1 from both sides.

$$\frac{10}{3}x<-\frac{6}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{10}{3}x<-\frac{6}{5}-\frac{5}{5}$$

Since -\frac{6}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{3}x<\frac{-6-5}{5}$$

Subtract 5 from -6 to get -11.

$$\frac{10}{3}x<-\frac{11}{5}$$

Multiply both sides by \frac{3}{10}, the reciprocal of \frac{10}{3}. Since \frac{10}{3} is positive, the inequality direction remains the same.

$$x<-\frac{11}{5}\times \frac{3}{10}$$

Multiply -\frac{11}{5} times \frac{3}{10} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{-11\times 3}{5\times 10}$$

Do the multiplications in the fraction \frac{-11\times 3}{5\times 10}.

$$x<\frac{-33}{50}$$

Fraction \frac{-33}{50} can be rewritten as -\frac{33}{50} by extracting the negative sign.

$$x<-\frac{33}{50}$$