Question

Mai and Han solve the equation √3x+2= √-2x-3 using Desmos. Mai says the answer is 4.172, and Han says the answer is 3.81. Who is correct, and why?

Answer 1

Both Mai and Han are incorrect. The equation √(3x+2) = √(-2x-3) can be solved by squaring both sides, which yields a solution of x = -1 after simplifying and solving the resulting quadratic equation.

Step-by-step explanation:

The equation √(3x+2) = √(-2x-3) suggests a square root equation where each side of the equation is under a square root. To solve it, we need to square both sides to remove the square roots and then solve the resulting quadratic equation.

First, both sides of the equation are squared:

1. 
   
3. (√(3x + 2))^2 = (√(-2x - 3))^2
4. 
   
6. 3x + 2 = -2x - 3

Next, we collect like terms:

1. 
   
3. Add 2x to both sides: 5x + 2 = -3
4. 
   
6. Subtract 2 from both sides: 5x = -5
7. 
   
9. Divide by 5: x = -1

Thus, the solution to the equation is x = -1, which means that both Mai's answer of 4.172 and Han's answer of 3.81 are incorrect. It is also important to check if the obtained solution is valid by substituting it back into the original equation to ensure both sides of the equation correspond when the variable is replaced with the solution.