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Solve for x: -4(3x + 10) - 2 = 54.

A. x = -4
B. x = -8
C. x = 4
D. x = 8

3 answers

To solve the equation \(-4(3x + 10) - 2 = 54\), we can follow these steps:

  1. Distribute \(-4\) to both terms inside the parentheses: \[ -4(3x) - 4(10) - 2 = 54 \] This simplifies to: \[ -12x - 40 - 2 = 54 \]

  2. Combine the constant terms on the left side: \[ -12x - 42 = 54 \]

  3. Add \(42\) to both sides to isolate the \(x\) term: \[ -12x = 54 + 42 \] \[ -12x = 96 \]

  4. Now divide both sides by \(-12\): \[ x = \frac{96}{-12} \] \[ x = -8 \]

Thus, the solution for \(x\) is \(-8\).

The correct answer is \(B. x = -8\).

are you sure this is correct

Yes, let's verify the solution step by step again to ensure accuracy.

We start with the equation:

\[ -4(3x + 10) - 2 = 54 \]

Step 1: Distribute -4

\[ -4 \cdot 3x - 4 \cdot 10 - 2 = 54 \] \[ -12x - 40 - 2 = 54 \]

Step 2: Combine constants on the left side

\[ -12x - 42 = 54 \]

Step 3: Add 42 to both sides

\[ -12x = 54 + 42 \] \[ -12x = 96 \]

Step 4: Divide by -12

\[ x = \frac{96}{-12} \] \[ x = -8 \]

The calculation confirms that \(x = -8\) is correct.

So the answer remains:

B. x = -8.

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