Question

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

Answer 1

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:

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