Let's solve the equation:

\[
3 - 4x + 5 = 2(8 - 2x)
\]

### Step 1: Simplify both sides of the equation.
First, expand the right-hand side:

\[
3 - 4x + 5 = 2 \times 8 - 2 \times 2x
\]
\[
3 - 4x + 5 = 16 - 4x
\]

Now, simplify the left-hand side:

\[
(3 + 5) - 4x = 16 - 4x
\]
\[
8 - 4x = 16 - 4x
\]

### Step 2: Remove like terms.
Add \(4x\) to both sides to eliminate the \(-4x\) term from both sides:

\[
8 = 16
\]

### Conclusion:
This equation results in a contradiction (\(8 \neq 16\)). Therefore, the equation has **no solution**.

Would you like more details on any step, or have any questions?

### Related Questions:
1. What happens if we have a different coefficient on \(x\) in this equation?
2. How can we tell an equation has no solution before solving it?
3. How does this equation compare to one with infinitely many solutions?
4. What if the equation was \(3 - 4x + 5 = 2(8 - 3x)\)?
5. How would the solution change if there were constants only on one side?

### Tip:
Equations that result in contradictions like \(8 = 16\) are inconsistent, meaning they have no solution. Always check for such cases when simplifying equations.

Learn how to solve the linear equation 3 - 4x + 5 = 2(8 - 2x) step-by-step. This problem involves simplifying both sides of the equation and identifying contradictions. Understand why this equation has no solution and explore related algebraic concepts. Suitable for students in Grades 8-10.

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