Questions: What is the value of 2x in this equation? 5x-2(2x-1)=2(3x-4) (A) 6 (C) 1.2 (B) 4 (D) -20

Transcript text: 3. What is the value of $2 x$ in this equation? \[ 5 x-2(2 x-1)=2(3 x-4) \] (A) 6 (C) 1.2 (B) 4 (D) -20

Solution

Solution Steps

To find the value of $2x$, we first need to solve the given equation for $x$. Start by expanding and simplifying both sides of the equation. Then, isolate $x$ to find its value. Once $x$ is determined, calculate $2x$.

Step 1: Set Up the Equation

We start with the equation given in the problem: \[ 5x - 2(2x - 1) = 2(3x - 4) \]

Step 2: Expand and Simplify

Expanding both sides, we have: \[ 5x - (4x - 2) = 6x - 8 \] This simplifies to: \[ 5x - 4x + 2 = 6x - 8 \] which further simplifies to: \[ x + 2 = 6x - 8 \]

Step 3: Isolate $x$

Rearranging the equation to isolate $x$: \[ 2 + 8 = 6x - x \] This gives: \[ 10 = 5x \] Thus, we find: \[ x = 2 \]

Step 4: Calculate $2x$

Now, we calculate $2x$: \[ 2x = 2 \cdot 2 = 4 \]