Match the description of the one variable equation with the number of solutions it will have.(4 points)

Question

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

Answer 1

Let's analyze each of the equations to determine the number of solutions they have:

1. Equation: x - 7 = 7 - x

   • Rearranging gives: x + x = 7 + 7 → 2x = 14 → x = 7
   • Number of solutions: 1

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

   • Expanding gives: 3x + 15 = 3x + 5
   • Subtracting 3x from both sides gives: 15 = 5
   • This is a false statement, thus there are no solutions.
   • Number of solutions: 0

3. Equation: 10 - x = 25

   • Rearranging gives: -x = 25 - 10 → -x = 15 → x = -15
   • Number of solutions: 1

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

   • Expanding gives: 2x + 8 = 2x + 8
   • This simplifies to the true statement 8 = 8, which is always true.
   • Number of solutions: infinite solutions

So the matches are:

• x - 7 = 7 - x: 1 solution
• 3(x + 5) = 3x + 5 : 0 solutions
• 10 - x = 25: 1 solution
• 2(x + 4) = 2x + 5 + 3: infinite solutions

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