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:

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