Question

Question 17

Determine the number of solutions for the equation below.

3/2(4−8x)+5x=1−7x
(1 point)
Responses

Infinitely many solutions
Infinitely many solutions

No solution
No solution

One solution

Answer 1

To solve the equation \(\frac{3}{2}(4 - 8x) + 5x = 1 - 7x\), we start by simplifying both sides step by step.

1. Distribute \(\frac{3}{2}\) on the left side:
\[
\frac{3}{2} \cdot 4 - \frac{3}{2} \cdot 8x = 6 - 12x
\]
So the equation becomes:
\[
6 - 12x + 5x = 1 - 7x
\]

2. Combine like terms on the left side:
\[
6 - 7x = 1 - 7x
\]

3. Add \(7x\) to both sides:
\[
6 = 1
\]

This statement \(6 = 1\) is a contradiction, which indicates that there is no solution to the equation.

Thus, the answer is:

**No solution**.