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Gwyneth begins solving for x in the equation 2 (x minus 4) = 5 (4 minus 2 x) + 4 x. After applying the distributive property and combining like terms, which equation will Gwyneth have to solve in order to determine the value of x?

2 x minus 8 = 20 minus 14 x
2 x minus 8 = 20 minus 6 x
2 x minus 4 = 20 + 2 x
2 x minus 4 = 20 minus 6 x

1 answer

Let's start by solving the equation step by step.

The original equation is:

\[ 2(x - 4) = 5(4 - 2x) + 4x. \]

  1. Apply the distributive property on both sides:

    • Left side: \[ 2(x - 4) = 2x - 8. \]
    • Right side: \[ 5(4 - 2x) = 20 - 10x, \] so \[ 5(4 - 2x) + 4x = 20 - 10x + 4x = 20 - 6x. \]

  2. Now we can rewrite the equation: \[ 2x - 8 = 20 - 6x. \]

So, now we have the equation:

\[ 2x - 8 = 20 - 6x. \]

From the options given, the correct one is:

\[ 2x - 8 = 20 - 6x. \]