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

To match the descriptions of the one variable equations with the number of solutions, let's analyze each equation:

1. Equation: x − 7 = 7 − x

   This simplifies to:

   • x + x = 7 + 7
   • 2x = 14
   • x = 7

   Number of solutions: 1 (one solution)

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

   This simplifies to:

   • 3x + 15 = 3x + 5
   • 15 = 5 (which is false)

   Number of solutions: 0 (no solution)

3. Equation: 10 − x = 25

   This simplifies to:

   • -x = 25 - 10
   • -x = 15
   • x = -15

   Number of solutions: 1 (one solution)

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

   This simplifies to:

   • 2x + 8 = 2x + 8
   • 8 = 8 (which is always true)

   Number of solutions: Infinite (infinitely many solutions)

Now, let's summarize the matches:

• 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

This gives us the matching descriptions.