Final answer:
To solve the inequality 5/14x > 50/77, cross-multiply to remove the fractions and simplify, which gives us x > 0.55 as the solution.
Step-by-step explanation:
To solve the inequality 5/14x > 50/77, we need to find the value of x that satisfies the inequality. To do this, we can start by simplifying both sides of the inequality if possible. Since both numbers on the right and left side of the inequality are fractions, we can cross-multiply to eliminate the denominators:
- Multiply both sides by 14x to get rid of the fraction on the left: 5 < 50/77 × 14x
- Similarly, multiply both sides by 77 to get rid of the fraction on the right: 5/14 × 77 < 50x
After the cross-multiplication, we have 385 < 700x. Dividing both sides by 700 to isolate x gives us:
x > 385/700
When we simplify the fraction, we have:
x > 0.55
Therefore, for the inequality 5/14x > 50/77, the solution is x > 0.55.