Match the description of the one variable equation with the number of solutions it will have.

Question

x−7=7−x
3(x+5)=3x+5
10−x=25
2(x+4)=2x+5+3

Answer 1

Let's analyze each equation one by one to determine the number of solutions:

1. Equation: \( x - 7 = 7 - x \)

   Rearranging: \( x + x = 7 + 7 \) leads to \( 2x = 14 \)
   Thus, \( x = 7 \)

   Number of solutions: 1 solution

2. Equation: \( 3(x + 5) = 3x + 5 \)

   Rearranging: Expanding the left side gives \( 3x + 15 = 3x + 5 \).
   Subtract \( 3x \) from both sides: \( 15 = 5 \), which is false.

   Number of solutions: 0 solutions (inconsistent)

3. Equation: \( 10 - x = 25 \)

   Rearranging: \( -x = 25 - 10 \) leads to \( -x = 15 \)
   Thus, \( x = -15 \)

   Number of solutions: 1 solution

4. Equation: \( 2(x + 4) = 2x + 5 + 3 \)

   Rearranging: Expanding the left side gives \( 2x + 8 = 2x + 8 \).
   Subtracting \( 2x \) from both sides yields \( 8 = 8 \), which is always true.

   Number of solutions: Infinitely many solutions (dependent)

Summary:

• \( x - 7 = 7 - x \) → 1 solution
• \( 3(x + 5) = 3x + 5 \) → 0 solutions
• \( 10 - x = 25 \) → 1 solution
• \( 2(x + 4) = 2x + 5 + 3 \) → Infinitely many solutions