Linear equations and inequalities

Solve $5x - 7 = 2x + 8$.

Solve $\dfrac{x + 2}{3} = \dfrac{x - 1}{2}$.

Which of these equations have no solution? (Choose all that apply.)

Ravi starts with the equation $x = 5$. He multiplies both sides by $0$, gets $0 = 0$, and concludes that every number is a solution. What went wrong?

Solve $4 - 2x > 10$.

In Manila, one phone-repair shop charges $150$ pesos plus $80$ pesos per hour of work. Another charges $50$ pesos plus $100$ pesos per hour. For how many hours of work do the two shops charge the same?

Ama has $50$ cedis. She buys a bus ticket for $8$ cedis and wants to spend the rest on mangoes at $4$ cedis each. What is the largest number of mangoes she can buy?

Which Lean statement correctly says "multiplying both sides of an inequality by a negative number reverses it"?

Write solve_linear(a, b, c, d) for the equation $ax + b = cx + d$ with integer coefficients. Return the solution as a Fraction if there is exactly one, the string "none" if there is no solution, and "all" if every number is a solution.

Kwame claims he has found a linear equation $ax + b = cx + d$ whose solutions are exactly $x = 1$ and $x = 2$. Which argument shows this is impossible?