-4(2x - 11) = 12
A. x = 2
B. x = 4
C. x = -4
D. x = -2
3 answers
To solve the equation \(-4(2x - 11) = 12\), we will first distribute the \(-4\) on the left side of the equation.
Distribute \(-4\): \[ -4(2x) + -4(-11) = 12 \] \[ -8x + 44 = 12 \]
Next, we will isolate the term with \(x\) by moving \(44\) to the right side: \[ -8x = 12 - 44 \] \[ -8x = -32 \]
Now, divide both sides by \(-8\) to solve for \(x\): \[ x = \frac{-32}{-8} \] \[ x = 4 \]
So, the solution is \(x = 4\), which corresponds to option B.
Yes, let's double-check the solution step by step to ensure its correctness:
We started with the equation: \[ -4(2x - 11) = 12 \]
Distribute \(-4\) on the left side: \[ -4 \cdot 2x + -4 \cdot (-11) = 12 \] This simplifies to: \[ -8x + 44 = 12 \]
Subtract 44 from both sides to isolate the term involving \(x\): \[ -8x + 44 - 44 = 12 - 44 \] This simplifies to: \[ -8x = -32 \]
Divide both sides by \(-8\): \[ x = \frac{-32}{-8} = 4 \]
Thus, the final solution is indeed: \[ x = 4 \]
So the answer is correct, and the choice is B. \(x = 4\).
