Question

Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.

7 x + 1 = 7 x+ 1. 3 x + 2 = 3 x minus 2. 4 x + 1 = 3 x + 8. negative 2 x minus 1 = negative 2 x minus 1.

Which of Jubal’s equations has no solution?
7 x + 1 = 7 x+ 1
3 x + 2 = 3 x minus 2
4 x + 1 = 3 x + 8
negative 2 x minus 1 = negative 2 x minus 1

Answer 1

To determine which of Jubal's equations has no solution, we can analyze each equation one by one to see if they hold true for all values of \(x\) or if they lead to a contradiction.

1. **Equation:** \(7x + 1 = 7x + 1\)

This equation is true for all \(x\), as both sides are identical.

2. **Equation:** \(3x + 2 = 3x - 2\)

Rearranging gives us:
\[
3x + 2 - 3x = -2
\]
\[
2 = -2
\]
This is a contradiction. So, this equation has no solution.

3. **Equation:** \(4x + 1 = 3x + 8\)

Rearranging gives us:
\[
4x - 3x = 8 - 1
\]
\[
x = 7
\]
This equation has a solution (\(x = 7\)).

4. **Equation:** \(-2x - 1 = -2x - 1\)

This equation is also true for all \(x\), as both sides are identical.

From the analysis, we find that the equation **\(3x + 2 = 3x - 2\)** is the only one with no solution.