More Than

You have 12 saved and you add 5 every week. After how many weeks will you have more than 42? Call the number of weeks $x$. The savings after $x$ weeks are $12+5x$. "More than 42" leaves 42 out, so the sign is a strict >:

$$12+5x > 42$$

$$5x > 30$$

$$x > 6$$

The number of weeks must be more than 6, so the first week that works is week 7. At exactly 6 weeks you have exactly 42, which is not more than 42. "More than" leaves the endpoint out. "At least" would include it, and then week 6 would count.

To write an inequality from words, read the phrase twice. Put the quantity from the story on the left of the sign and the limit on the right. Choose the sign from the words. Then solve it like any other inequality.