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For which equation is the order of steps to first divide both sides by 6 and then to add 8 to both sides?

6 ( x + 8 ) = 48

8 ( x - 6 ) = 48

6 ( x - 8 ) = 48

6x - 8 = 48

1 answer

To determine which equation allows us to first divide both sides by 6 and then add 8 to both sides, let's analyze each equation step by step.

  1. Equation 1: \(6 (x + 8) = 48\)

    • Divide both sides by 6:
      \[ x + 8 = 8 \]
    • Now add 8 to both sides:
      \[ x + 8 + 8 = 8 + 8 \]
      \[ x + 8 = 16 \]
    • This is valid since we can still apply the steps correctly.

  2. Equation 2: \(8 (x - 6) = 48\)

    • Divide both sides by 8:
      \[ x - 6 = 6 \]
    • To add 8 to both sides:
      \[ x - 6 + 8 = 6 + 8 \]
      \[ x + 2 = 14 \]
    • This does not follow the step of dividing by 6 first.

  3. Equation 3: \(6 (x - 8) = 48\)

    • Divide both sides by 6:
      \[ x - 8 = 8 \]
    • Add 8 to both sides:
      \[ x - 8 + 8 = 8 + 8 \]
      \[ x = 16 \]
    • This is valid since we performed the operations correctly.

  4. Equation 4: \(6x - 8 = 48\)

    • Divide both sides by 6:
      \[ x - \frac{8}{6} = 8 \]
      \[ x - \frac{4}{3} = 8 \]
    • Add 8 to both sides: \[ x = 8 + \frac{4}{3} \]
    • Adding 8 directly doesn’t lead correctly to our steps.

The only equation for which the steps make sense (first dividing by 6 and then adding 8 to both sides) is Equation 1: \(6 (x + 8) = 48\) and Equation 3: \(6 (x - 8) = 48\).

Therefore, both Equation 1 and Equation 3 allow for the operations in the specified order..