Solve this equation. Identify any extraneous solution. Show all steps.
x = [3x + 40]
Transpose 3x term.
x-3x = 40
Combine terms.
-2x = 40
Divide both sides by -2.
To solve the equation x = 3x + 40, we will follow these steps:
Step 1: Start by simplifying the equation.
x = 3x + 40
Step 2: Rewrite the equation by isolating the variable on one side.
Subtract 3x from both sides:
x - 3x = 3x - 3x + 40
-2x = 40
Step 3: Simplify the equation further by dividing both sides by -2 to solve for x.
Divide both sides by -2:
(-2x)/(-2) = 40/(-2)
x = -20
Step 4: Check for extraneous solutions.
Plug the value of x (x = -20) back into the original equation and see if it holds true:
-20 = 3(-20) + 40
-20 = -60 + 40
-20 = -20
Since the equation -20 = -20 is true, the solution x = -20 is valid and not extraneous.
Therefore, the solution to the equation x = 3x + 40 is x = -20, with no extraneous solutions.