Question

Below is an attempt to solve the equation 4x - 8 - 2x + 6. Identify if there is a mistake in the work and in which step the mistake occurred.
4x - 8 = 2x + 6
Step 1: Subtract 2x from both sides of the equation
4.-2-8=2x-2x+6
Step 2: Simplify
2x - 8=6
Step 3: Add 8 to both sides of the equation
2x - 8+8=6+8
Step 4: Simplify
2x = 14
Step 5: Divide both sides of the equation by 2
2x/2 = 14/2
Step 6: Simplify
X = 7

A. The mistake was in Step 3 when adding 8 to both sides of the equation.
B. The mistake was made in Step 1 when subtracting 2x from both sides of the equation.
C. The mistake was made in Step 5 when dividing both sides of the equation by 2.
D. There is no mistake.

Answer 1

Let's analyze the steps to identify if there is a mistake.

You started with the equation:
\[ 4x - 8 = 2x + 6 \]

**Step 1:** You subtracted \( 2x \) from both sides:
\[ 4x - 2x - 8 = 2x - 2x + 6 \]
This simplifies to:
\[ 2x - 8 = 6 \]
This step is correct.

**Step 2:** You simplified:
\[ 2x - 8 = 6 \]
This is also correct.

**Step 3:** You added 8 to both sides:
\[ 2x - 8 + 8 = 6 + 8 \]
This simplifies to:
\[ 2x = 14 \]
This step is correct.

**Step 4:** You divided both sides by 2:
\[ \frac{2x}{2} = \frac{14}{2} \]
This simplifies to:
\[ x = 7 \]
This step is also correct.

After reviewing all steps, there are no mistakes in any of the steps provided. Therefore, the answer is:

D. There is no mistake.