Question

4x Select the equation has no solution.
•×

2x +17-7x-6 = 8 - 10x - 19 + 5x


7 + 16x+1-4x=24 + 8x -9 + 3x

C
9x -3 + 2x + 20 = 15 + 4x + 2 + 7x


12- 6x +4-x=3 + 8x + 13 - 11x

Answer 1

To determine which equation has no solution, we need to simplify each equation and find if they lead to a contradiction.

1. **Equation 1:** \( 2x + 17 - 7x - 6 = 8 - 10x - 19 + 5x \)

Simplifying both sides:
- Left side: \( 2x - 7x + 17 - 6 = -5x + 11 \)
- Right side: \( 8 - 19 + 5x - 10x = -11 - 5x \)

Setting them equal:
\(-5x + 11 = -11 - 5x\)

If we add \(5x\) to both sides:
\(11 = -11\), which is a contradiction. **(No solution)**

2. **Equation 2:** \( 7 + 16x + 1 - 4x = 24 + 8x - 9 + 3x \)

Simplifying both sides:
- Left side: \( 7 + 1 + 16x - 4x = 8 + 12x \)
- Right side: \( 24 - 9 + 8x + 3x = 15 + 11x \)

Setting them equal:
\( 8 + 12x = 15 + 11x \)

If we subtract \(11x\) from both sides:
\(8 + x = 15\)

Subtracting 8 gives:
\(x = 7\), which is a solution.

3. **Equation 3:** \( 9x - 3 + 2x + 20 = 15 + 4x + 2 + 7x \)

Simplifying both sides:
- Left side: \( 9x + 2x - 3 + 20 = 11x + 17 \)
- Right side: \( 15 + 4x + 2 + 7x = 15 + 11x \)

Setting them equal:
\( 11x + 17 = 15 + 11x \)

Subtracting \(11x\) from both sides:
\(17 = 15\), which is a contradiction. **(No solution)**

4. **Equation 4:** \( 12 - 6x + 4 - x = 3 + 8x + 13 - 11x \)

Simplifying both sides:
- Left side: \( 12 + 4 - 6x - x = 16 - 7x \)
- Right side: \( 3 + 13 + 8x - 11x = 16 - 3x \)

Setting them equal:
\( 16 - 7x = 16 - 3x \)

Subtracting \(16\) from both sides:
\(-7x = -3x\)

Adding \(3x\) to both sides gives:
\(-4x = 0\) or \(x = 0\), which is a solution.

After evaluating all four equations, we find that:

**Equations 1 and 3 have no solution.**

However, if you had to select just one, it would depend on which option is provided in your original question. Please clarify if you are looking for the first one found or if both are acceptable.