It looks like the problem here involves setting up inequalities to model a budget constraint for Han. Since Han's budget is up to $65, this can be represented as an inequality rather than an equation. Let's break down the two tasks given:

1. Choosing the correct inequality: The inequality $0.70p + 0.1w + 8g \leq 65$ is appropriate because it indicates that Han’s total expenditure on $p$, $w$, and $g$ cannot exceed $65. The symbol $\leq$ is correct since $65 is a limit and not an exact spending amount, meaning he can spend any amount up to but not over $65.

2. Writing the inequality for all variables $p$, $w$, $q$: The second answer should actually repeat the inequality correctly with the form $0.70p + 0.1w + 8g \leq 65$, as it states the relationship among the total expenditure terms with the same budget constraint.

It seems that the answer provided repeats the constraint but does not need the second box to be filled differently if the goal is to model the same relationship with the inequality.

Would you like a further breakdown of how each coefficient (like 0.70, 0.1, and 8) relates to each variable or help with interpreting constraints in budgeting problems?

Here are five related questions to expand your understanding:

1. How would the inequality change if Han's budget increased to $70?
2. What does each coefficient (e.g., 0.70) represent in terms of cost per unit of each variable?
3. Can we solve for specific values of $p$, $w$, and $g$ if given additional constraints?
4. How would you represent a situation where Han has to spend exactly $65 instead of "up to"?
5. How would adding another variable (like a tax) impact the inequality?

Tip: Always remember that inequalities allow flexibility within limits, which is helpful when setting budget constraints that aren't fixed but rather have an upper limit.