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Use the distributive property to simplify and solve for x.

2(2x - 5) = 14

(1 point)
Responses

x = 6
x = 6

x = 3
x = 3

x = 5
x = 5

x = 19

1 answer

To solve the equation \( 2(2x - 5) = 14 \) using the distributive property, follow these steps:

  1. Distribute the 2 on the left side: \[ 2 \cdot 2x - 2 \cdot 5 = 14 \] This simplifies to: \[ 4x - 10 = 14 \]

  2. Next, add 10 to both sides to isolate the term with \( x \): \[ 4x - 10 + 10 = 14 + 10 \] This simplifies to: \[ 4x = 24 \]

  3. Now, divide both sides by 4 to solve for \( x \): \[ x = \frac{24}{4} \] This simplifies to: \[ x = 6 \]

Thus, the solution is \( \boxed{6} \).