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Below is an attempt to solve the equation 4x−8=2x+64x−8=2x+6 . Identify if there is a mistake in the work and in which step the mistake occurred. 4x−8=2x+64x−8=2x+6 Step 1: Subtract 2x from both sides of the equation 4x−2x−8=2x−2x+64x−2x−8=2x−2x+6 Step 2: Simplify 2x−8=62x−8=6 Step 3: Add 8 to both sides of the equation 2x−8+8=6+82x−8+8=6+8 Step 4: Simplify 2x=142x=14 Step 5: Divide both sides of the equation by 2 2x2=1422x2=142 Step 6: Simplify x=7x=7 (1 point) Responses The mistake was made in Step 1 when subtracting 2x from both sides of the equation. The mistake was made in Step 1 when subtracting 2x from both sides of the equation. There is no mistake. There is no mistake. The mistake was made in Step 5 when dividing both sides of the equation by 2. The mistake was made in Step 5 when dividing both sides of the equation by 2. The mistake was in Step 3 when adding 8 to both sides of the equation.

1 answer

Let's analyze the provided steps of solving the equation \(4x - 8 = 2x + 6\) to find if there is a mistake.

  1. Original Equation: \(4x - 8 = 2x + 6\)

  2. Step 1: Subtract \(2x\) from both sides.

    • Left side: \(4x - 2x - 8 = 2x + 6 - 2x\)
    • Result: \(2x - 8 = 6\)
    • This step is correct.

  3. Step 2: Simplify the equation.

    • Result is \(2x - 8 = 6\)
    • This step is also correct.

  4. Step 3: Add 8 to both sides.

    • \((2x - 8) + 8 = 6 + 8\)
    • Result: \(2x = 14\)
    • This step is correct.

  5. Step 4: Divide both sides by 2.

    • \(\frac{2x}{2} = \frac{14}{2}\)
    • Result: \(x = 7\)
    • This step is correct.

Based on this analysis, all steps correctly follow from one another and adhere to algebraic principles. Thus, there are no mistakes in the calculations.

The correct response is: There is no mistake.