Solve 32x-3/5<7

$$3 \frac { 2 x - 3 } { 5 } < 7$$

Solve for x

$$x<\frac{22}{3}$$

Solution Steps

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

$$\frac{2x-3}{5}<\frac{7}{3}$$

Multiply both sides by 5. Since 5 is positive, the inequality direction remains the same.

$$2x-3<\frac{7}{3}\times 5$$

Express \frac{7}{3}\times 5 as a single fraction.

$$2x-3<\frac{7\times 5}{3}$$

Multiply 7 and 5 to get 35.

$$2x-3<\frac{35}{3}$$

Add 3 to both sides.

$$2x<\frac{35}{3}+3$$

Convert 3 to fraction \frac{9}{3}.

$$2x<\frac{35}{3}+\frac{9}{3}$$

Since \frac{35}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$2x<\frac{35+9}{3}$$

Add 35 and 9 to get 44.

$$2x<\frac{44}{3}$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x<\frac{\frac{44}{3}}{2}$$

Express \frac{\frac{44}{3}}{2} as a single fraction.

$$x<\frac{44}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x<\frac{44}{6}$$

Reduce the fraction \frac{44}{6} to lowest terms by extracting and canceling out 2.

$$x<\frac{22}{3}$$