Solve for *x*.

14x−12(4x+6)=3(x−4)−1814x−12(4x+6)=3(x−4)−18

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Let's solve the equation step by step.

The equation given is:

\[ 14x - 12(4x + 6) = 3(x - 4) - 18 \]

### Step 1: Distribute the constants
Distribute \(-12\) on the left-hand side and \(3\) on the right-hand side:

\[ 14x - 48x - 72 = 3x - 12 - 18 \]

### Step 2: Simplify both sides
Combine like terms on both sides of the equation:

\[ (14x - 48x) - 72 = 3x - 30 \]

\[ -34x - 72 = 3x - 30 \]

### Step 3: Move all \(x\) terms to one side
Add \(34x\) to both sides of the equation to get all the \(x\) terms on one side:

\[ -72 = 37x - 30 \]

### Step 4: Move constants to the other side
Add \(30\) to both sides of the equation to move the constants to one side:

\[ -72 + 30 = 37x \]

\[ -42 = 37x \]

### Step 5: Solve for \(x\)
Finally, divide both sides by 37 to solve for \(x\):

\[ x = \frac{-42}{37} \]

So, the solution is:

\[ x = \frac{-42}{37} \]

If you need more details or have any questions, feel free to ask!

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Here are 8 related questions you might find helpful:
1. What is the importance of distributing constants in algebraic equations?
2. How can you verify the solution to an equation?
3. What are the common mistakes to avoid when solving linear equations?
4. How do you simplify expressions with multiple variables?
5. What is the next step after solving a linear equation?
6. Can this equation be solved graphically, and how?
7. What are other methods to solve linear equations besides algebraic manipulation?
8. How do you handle equations with fractions or decimals?

**Tip:** Always double-check your distribution and sign changes when solving equations; small mistakes can lead to incorrect solutions.

Explore how to solve the linear equation 14x - 12(4x + 6) = 3(x - 4) - 18 with a detailed step-by-step solution. This problem involves linear equations and the distributive property, suitable for high school students.

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