Can AI solve my math homework?

The made-up sample:

• [PROBLEM]Find the value of x that satisfies the equation 2(x - 4) + 7 = 3x - 5.
• [MY WORK]I expanded the left side: 2x - 8 + 7 = 2x - 1. Then I thought to combine like terms, giving 2x - 1 = 3x - 5. I moved terms around and got -1 = x - 5, so x = 4.
• [STEP]I'm stuck on how to correctly isolate x after moving terms; I'm not sure if I made an error in combining the constants.

• ✓MUST give one hint or step at a time and wait for my attempt
• ✓MUST show your arithmetic so I can check it
• ✓NEVER skip steps or give the final answer until I've tried
• ✓Don't give the final answer right away
• ✓Didn't make up details we never gave it

What came back (excerpt):

My first hint is to try to get all the x terms on one side of the equation. To do this, you can subtract 2x from both sides of the equation.

You've made a great start by expanding the left side of the equation. Now, let's take a closer look at the equation you got after combining like terms: 2x - 1 = 3x - 5.

My first hint is to try to get all the x terms on one side of the equation. To do this, you can subtract 2x from both sides of the equation. Here's what that would look like:

2x - 1 = 3x - 5
Subtracting 2x from both sides:
2x - 2x - 1 = 3x - 2x - 5

Now it's your turn! See if you can simplify the equation and take it from there.

Ensure the response sticks to a single-step hint and includes arithmetic.

The made-up sample (a messier one):

• [PROBLEM]Find the area between the curves y = x^2 and y = 2x + 3 from x = -1 to x = 3.
• [MY WORK]My attempt: I solved x^2 = 2x + 3, got x = -1 and 3. I assumed 2x+3 is above x^2, so I set up ∫_{-1}^{3} [(2x+3) - x^2] dx. I found antiderivative (x^2 + 3x - x^3/3) and evaluated, getting about 20/3.
• [STEP]I'm not sure if 2x+3 really stays on top of x^2 for the whole interval, especially near x = -1. How can I confirm which function is upper?

• ✓Must give one hint or step at a time and wait for my attempt
• ✓Must show arithmetic so I can check it
• ✓Never give the final answer until I've tried
• ✓Never skip steps
• ✓Didn't make up details we never gave it

What came back (excerpt):

First, let's calculate the values of both functions at x = -1: For y = x^2, we have y = (-1)^2 = 1.

To confirm which function is the upper curve, let's evaluate both functions at the endpoints of the interval and at a point in between. We already know the endpoints are x = -1 and x = 3.

First, let's calculate the values of both functions at x = -1:
For y = x^2, we have y = (-1)^2 = 1.
For y = 2x + 3, we have y = 2(-1) + 3 = -2 + 3 = 1.

Now, let's calculate the values of both functions at x = 3:
For y = x^2, we have y = (3)^2 = 9.
For y = 2x + 3, we have y = 2(3) + 3 = 6 + 3 = 9.

We see that at both endpoints, the values of the two functions are equal, which is expected since we found these points by solving x^2 = 2x + 3. 

Next, let's pick a point in between, say x = 0, to see which function is greater:
For y = x^2, we have y = (0)^2 = 0.
For y = 2x + 3, we have y = 2(0) + 3 = 3.

Now it's your turn. What do you observe about the values at x = 0, and how does this help you understand the relationship between the two curves?

Check that only a single hint is provided before the user responds.