Solve 16x-4-5+x<2-4/3x

$$16x-4-5+x < 2- \frac{ 4 }{ 3 } x$$

Solve for x

$$x<\frac{3}{5}$$

Solution Steps

Subtract 5 from -4 to get -9.

$$16x-9+x<2-\frac{4}{3}x$$

Combine 16x and x to get 17x.

$$17x-9<2-\frac{4}{3}x$$

Add \frac{4}{3}x to both sides.

$$17x-9+\frac{4}{3}x<2$$

Combine 17x and \frac{4}{3}x to get \frac{55}{3}x.

$$\frac{55}{3}x-9<2$$

Add 9 to both sides.

$$\frac{55}{3}x<2+9$$

Add 2 and 9 to get 11.

$$\frac{55}{3}x<11$$

Multiply both sides by \frac{3}{55}, the reciprocal of \frac{55}{3}. Since \frac{55}{3} is positive, the inequality direction remains the same.

$$x<11\times \frac{3}{55}$$

Express 11\times \frac{3}{55} as a single fraction.

$$x<\frac{11\times 3}{55}$$

Multiply 11 and 3 to get 33.

$$x<\frac{33}{55}$$

Reduce the fraction \frac{33}{55} to lowest terms by extracting and canceling out 11.

$$x<\frac{3}{5}$$