Solving the Equation $3x - 14 = 4$ for $x$

The problem asks us to find the value of the variable $x$ that satisfies the equation $3x - 14 = 4$. This is a basic linear equation, and we can solve it by isolating $x$ on one side of the equation.

Step-by-Step Solution

1. Start with the given equation:

   $3x - 14 = 4$

2. Isolate the term with $x$: To get the term $3x$ by itself, we need to eliminate the $-14$. We do this by adding $14$ to both sides of the equation.

   $3x - 14 + 14 = 4 + 14$

   Simplify:

   $3x = 18$

3. Solve for $x$: Now, $x$ is multiplied by $3$. To find the value of $x$, we divide both sides of the equation by $3$.

   $\frac{3x}{3} = \frac{18}{3}$

   Simplify:

   $x = 6$

Equation Analysis and Options Verification

We followed the standard algebraic steps to solve the equation $3x - 14 = 4$. The result is $x = 6$. Let's check this against the given options:

• Option 1: $-9$
• Option 2: $9$
• Option 3: $-6$
• Option 4: $6$

Our calculated value for $x$ is $6$, which matches Option 4.

Verification of the Solution

We can verify the answer by substituting $x=6$ back into the original equation:

$3(6) - 14 \stackrel{?}{=} 4$

$18 - 14 \stackrel{?}{=} 4$

$4 = 4$

Since the left side equals the right side, our solution $x=6$ is correct.