6. Write and solve the inequality. \( \frac{4}{7} \) times a number minus 8.5 is no more than 11.5

To write the inequality for the given expression, we let \( x \) represent the unknown number. The inequality can be expressed as: \[ \frac{4}{7}x - 8.5 \leq 11.5 \] Now, let's solve for \( x \). Start by isolating \( \frac{4}{7}x \): \[ \frac{4}{7}x \leq 11.5 + 8.5 \] Combining the right side gives us: \[ \frac{4}{7}x \leq 20 \] Next, multiply both sides by \( \frac{7}{4} \) to solve for \( x \): \[ x \leq 20 \times \frac{7}{4} \] Simplifying that: \[ x \leq 35 \] So the solution to the inequality is: \[ x \leq 35 \] --- Finding solutions to inequalities is like piecing together a fun puzzle where each move takes you closer to the final answer! In this case, isolating \( x \) required careful balancing, just like making sure all your party guests have the right amount of cake! Solving inequalities not only builds your algebra skills but also can be applied in real-life scenarios, such as budgeting! For instance, if you're planning to buy multiple items while staying under a certain budget, setting up and solving inequalities can help you determine how much each item can cost without exceeding your limits.