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: \( x - 7 = 7 - x \)

   Solving:

   • Rearranging gives: \( x + x = 7 + 7 \)
   • This simplifies to: \( 2x = 14 \)
   • Thus, \( x = 7 \)

   Number of solutions: 1 solution

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

   Solving:

   • Expanding the left side gives: \( 3x + 15 = 3x + 5 \)
   • Subtracting \( 3x \) from both sides results in: \( 15 = 5 \)
   • This statement is false.

   Number of solutions: 0 solutions

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

   Solving:

   • Rearranging gives: \( -x = 25 - 10 \)
   • Which simplifies to: \( -x = 15 \)
   • Thus, \( x = -15 \)

   Number of solutions: 1 solution

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

   Solving:

   • Expanding the left side gives: \( 2x + 8 = 2x + 8 \)
   • This results in a true statement (both sides are equal).

   Number of solutions: Infinite solutions (the equation is true for all values of \( x \))

Summary of Number of Solutions:

1. \( x - 7 = 7 - x \) → 1 solution
2. \( 3(x + 5) = 3x + 5 \) → 0 solutions
3. \( 10 - x = 25 \) → 1 solution
4. \( 2(x + 4) = 2x + 5 + 3 \) → Infinite solutions