Solve 52x-5div3<x+1

$$52x-5 \div 3 < x+1$$

Solve for x

$$x<\frac{8}{153}$$

Solution Steps

Subtract x from both sides.

$$52x-\frac{5}{3}-x<1$$

Combine 52x and -x to get 51x.

$$51x-\frac{5}{3}<1$$

Add \frac{5}{3} to both sides.

$$51x<1+\frac{5}{3}$$

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

$$51x<\frac{3}{3}+\frac{5}{3}$$

Since \frac{3}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$51x<\frac{3+5}{3}$$

Add 3 and 5 to get 8.

$$51x<\frac{8}{3}$$

Divide both sides by 51. Since 51 is positive, the inequality direction remains the same.

$$x<\frac{\frac{8}{3}}{51}$$

Express \frac{\frac{8}{3}}{51} as a single fraction.

$$x<\frac{8}{3\times 51}$$

Multiply 3 and 51 to get 153.

$$x<\frac{8}{153}$$