As a math teacher, I can relate to the sentiment of this comic. People regularly boast to me about how bad they are at math (especially algebra), and still, they are successful in life. Much like the young woman in the comic, these people seem to believe that they were lied to about the utility of math, and they are resentful about it. Maybe lied is too strong a word, but perhaps we do misrepresent the purposes behind the math taught in schools.
Because I was teaching some algebra to middle school students twenty years ago, I remember how I responded to the question, "When will I ever use this?" Therefore, I have a theory about what might have been going on in Miss Lenhart's Algebra classes in the late 80s/early 90s. I imagine it might have looked like one of these four scenarios (depending on what she tried before).
Has much changed? I mean, besides the fact that we now add cell phone contract problems into the mix. For the most part, students remain unimpressed as we tie ourselves in knots to demonstrate how they will need the math we teach in everyday life. That is why I suggest that when asked by students, "When will we ever use this?" that teachers respond truthfully.
I don't know when or if you will ever need this particular concept. It depends on what you do with your life and what technological advances are made in the future. But you know what you will need to be able to do, regardless? You will need to problem solve. You will need to think critically (reason and prove). You will need to be able to communicate quantitative thinking to others. You will need to use representations to support your thinking and share your thinking. And you will need to make connections in order to consolidate your understanding. Mathematics is a discipline that provides opportunities to practice and strengthen all of these skills. So, as we solve for x, I want you to monitor your thinking because that's what's really important.
That is how I learned to respond to my middle school math students. The NCTM Process Standards gave purpose to my math lessons, and the students bought into it. It worked for me because I finally believed in what I was teaching.