Solve the equation for x: 2x+b=c Check this process: Step 1: 2x+b−b=c−b Step 2: 2x=c−b Step 3: 2x−2=c−b−2 Step 4: x=c2−b−2 Check all of the choices that are true statements. (1 point) Responses There is no error in the process. There is no error in the process. The process has an error from step 1 to step 2 The process has an error from step 1 to step 2 The process has an error from step 2 to step 3 The process has an error from step 2 to step 3 The process has an error from step 3 to step 4
The process has an error from step 3 to step 4.
In step 3, subtracting 2 from both sides should give: 2x - 2 = c - b - 2.
However, in step 4, the equation is written as: x = c2 - b - 2, which is incorrect.
The process has an error from step 3 to step 4.
In step 3, the correct equation is 2x - 2 = c - b -2.
To solve for x, we need to isolate the variable on one side of the equation. Therefore, in step 4, the correct equation should be:
2x - 2 = c - b
Adding 2 to both sides of the equation gives us:
2x = c - b + 2
To get x by itself, we divide both sides of the equation by 2:
x = (c - b + 2) / 2
The correct steps to solve the equation 2x+b=c are as follows:
Step 1: Subtract b from both sides of the equation:
2x+b−b=c−b
This step correctly eliminates the b term from the left side of the equation.
Step 2: Simplify the equation:
2x=c−b
This step correctly combines like terms on the right side of the equation.
Step 3: Divide both sides by 2:
2x/2=(c−b)/2
This step should be performed to isolate x on one side of the equation. However, the division should be done on both sides, not just on the left side.
Step 4: Simplify further:
x=(c−b)/2
This step correctly solves for x.
Therefore, the correct answer is: The process has an error from step 3 to step 4.