Question

what is the solution to $\frac{5x}{9} > \frac{3}{7}$? \\$\circ$ $x geq \frac{5}{21}$ \\$\circ$ $x > \frac{15}{63}$ \\$\circ$ $x < \frac{27}{35}$ \\$\circ$ $x > \frac{27}{35}$

Explanation:

Step1: Start with the inequality

We have the inequality $\frac{5x}{9} > \frac{3}{7}$.

Step2: Multiply both sides by 9

To isolate the term with $x$, we multiply both sides of the inequality by 9. This gives us $5x > \frac{3\times9}{7}$, which simplifies to $5x > \frac{27}{7}$.

Step3: Divide both sides by 5

Now, we divide both sides of the inequality by 5 to solve for $x$. Using the rule that dividing by a positive number doesn't change the direction of the inequality, we get $x > \frac{27}{7\times5}$, which simplifies to $x > \frac{27}{35}$.

Answer:

$x > \frac{27}{35}$ (corresponding to the option "x > 27/35")