Final answer:
To solve the equation 3x - 4 = 24x + 3, subtract 24x from both sides, add 4 to both sides, and divide by -21 to solve for x. The solution is x = -1/3. Checking our solution by substituting it back into the original equation, we find that both sides are equal.
Step-by-step explanation:
To solve the equation 3x - 4 = 24x + 3, we want to isolate the variable x. First, we can combine like terms by subtracting 24x from both sides of the equation. This gives us -21x - 4 = 3. Next, we can add 4 to both sides to get -21x = 7. Finally, divide both sides by -21 to solve for x. The solution is x = -7/21, which simplifies to x = -1/3.
To check our solution, we can substitute x = -1/3 back into the original equation and see if both sides are equal. Plugging in x = -1/3, we have 3(-1/3) - 4 = 24(-1/3) + 3. This simplifies to -1 - 4 = -8 + 3, which becomes -5 = -5. Since both sides are equal, our solution x = -1/3 is correct.