Final answer:
The original equation 2x + 3x - 2 = 7x + 2 + 4 simplifies to -2x = 8 after combining like terms and rearranging, yielding a solution of x = -4.
Step-by-step explanation:
The student has presented an algebraic equation to solve. The first step is to eliminate terms where possible to simplify the equation, and then we will check if the answer is reasonable.
Let's solve the equation:
2x + 3x - 2 = 7x + 2 + 4
First, combine like terms on each side:
5x - 2 = 7x + 6.
Now, we'll move the variable terms to one side and the constant terms to the other side:
5x - 7x = 6 + 2
-2x = 8.
Next, we divide both sides by -2 to solve for x:
x = 8 / (-2)
x = -4.
So the solution to the equation is x = -4. To check that this is a reasonable answer, you can substitute -4 back into the original equation.