Questions: What is the solution to this equation? 3(4x+6)=9x+12 A. x=-10 B. x=10 C. x=-2 D. x=2

Transcript text: Question 2 of 10 What is the solution to this equation? \[ 3(4 x+6)=9 x+12 \] A. $x=-10$ B. $x=10$ C. $x=-2$ D. $x=2$

Solution

To solve the equation $3(4x + 6) = 9x + 12$, we first expand the left side of the equation. Then, we collect like terms and solve for $x$.

Step 1: Expand the Equation

We start with the equation: \[ 3(4x + 6) = 9x + 12 \] Expanding the left side gives: \[ 12x + 18 = 9x + 12 \]

Step 2: Rearrange the Equation

Next, we rearrange the equation to isolate $x$. Subtract $9x$ from both sides: \[ 12x - 9x + 18 = 12 \] This simplifies to: \[ 3x + 18 = 12 \]

Step 3: Solve for $x$

Now, we subtract 18 from both sides: \[ 3x = 12 - 18 \] This simplifies to: \[ 3x = -6 \] Dividing both sides by 3 gives: \[ x = -2 \]

The answer is $\boxed{x = -2}$.

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