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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

1 answer

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.