Solve 13x/4leq5x-8

$$\frac { 13 x } { 4 } \leq 5 x - 8$$

Solve for x

$$x\geq \frac{32}{7}$$

Solution Steps

Multiply both sides of the equation by 4. Since 4 is positive, the inequality direction remains the same.

$$13x\leq 20x-32$$

Subtract 20x from both sides.

$$13x-20x\leq -32$$

Combine 13x and -20x to get -7x.

$$-7x\leq -32$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x\geq \frac{-32}{-7}$$

Fraction \frac{-32}{-7} can be simplified to \frac{32}{7} by removing the negative sign from both the numerator and the denominator.

$$x\geq \frac{32}{7}$$