Question

Which equations have no solutions. Mark all that apply.This problem requires you to show your work.(2 points)Responses 7x+3−4x=3(x+1)7 x plus 3 minus 4 x is equal to 3 times open paren x plus 1 close paren2(x+2)=2x+22 times open paren x plus 2 close paren is equal to 2 x plus 25x+5=5(2x+2)5 x plus 5 is equal to 5 times open paren 2 x plus 2 close paren6(x+8)=6x+5 6 times open paren x plus 8 close paren is equal to 6 x plus 5

Answer 1

To determine which equations have no solutions, let's analyze each equation step by step.

1. **Equation: \(7x + 3 - 4x = 3(x + 1)\)**
- Simplify left side: \(3x + 3 = 3(x + 1)\)
- Expanding right side: \(3x + 3 = 3x + 3\)
- This is true for all values of \(x\). Thus, it has infinitely many solutions.

2. **Equation: \(2(x + 2) = 2x + 2\)**
- Expanding left side: \(2x + 4 = 2x + 2\)
- Subtracting \(2x\) from both sides: \(4 = 2\)
- This is a false statement, meaning this equation has **no solutions**.

3. **Equation: \(5x + 5 = 5(2x + 2)\)**
- Expanding right side: \(5x + 5 = 10x + 10\)
- Rearranging: \(5 = 5x + 10\) → \(5 - 10 = 5x\) → \(-5 = 5x\) → \(x = -1\)
- This equation has a solution.

4. **Equation: \(6(x + 8) = 6x + 5\)**
- Expanding left side: \(6x + 48 = 6x + 5\)
- Subtracting \(6x\) from both sides: \(48 = 5\)
- This is a false statement, meaning this equation has **no solutions**.

### Summary
The equations with no solutions are:

- \(2(x + 2) = 2x + 2\)
- \(6(x + 8) = 6x + 5\)

Thus, the final answers are:

- \(2(x + 2) = 2x + 2\)
- \(6(x + 8) = 6x + 5\)