Solve Linear Equation: 3+4x-2+4x=17 with Like Terms

To solve this problem, we'll follow these steps:

• Simplify the equation by combining like terms.
• Isolate $x$ on one side of the equation.
• Solve for $x$.

Now, let's work through each step:
First, simplify the expression on the left side of the equation:

$3 + 4x - 2 \cdot 1 + 4x = 17$

Calculate $2 \cdot 1$, which is $2$. Then, replace that in the equation:

$3 + 4x - 2 + 4x = 17$

Next, combine the constant terms $3$ and $-2$:

$(3 - 2) + 4x + 4x = 17$

This simplifies to:

$1 + 4x + 4x = 17$

Now, combine the $x$-terms:

$1 + 8x = 17$

Isolate the $x$-term by subtracting $1$ from both sides:

$8x = 17 - 1$

This simplifies to:

$8x = 16$

Finally, solve for $x$ by dividing both sides by $8$:

$x = \frac{16}{8}$

Which simplifies to:

$x = 2$

Therefore, the solution to the problem is $x = 2$.