How do I solve the equation 3x + 5 = 2x + 4x + 2 + 5x and represent the solution set on a number line?

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Solving the Equation

Let’s start by simplifying and solving the equation step by step:

Given Equation: 3x + 5 = 2x + 4x + 2 + 5x

  1. Combine like terms:
    • On the right side, combine the terms: 2x + 4x + 5x = 11x
  2. Now the equation looks like this:
    • 3x + 5 = 11x + 2
  3. Isolate x: Subtract 3x from both sides:
    • 5 = 11x – 3x + 2
  4. Which simplifies to:
    • 5 = 8x + 2
  5. Now, subtract 2 from both sides:
    • 5 – 2 = 8x
  6. So we have:
    • 3 = 8x
  7. Now, divide both sides by 8:
    • x = 3/8

Thus, the solution to the equation is x = 3/8.

Representing the Solution Set on a Number Line

To visualize the solution set on a number line, follow these steps:

  1. Draw a horizontal line to represent the number line.
  2. Mark points on the line for whole numbers, including zero.
  3. Locate the point 3/8 on the line, which is between 0 and 1.
  4. Indicate that this is the solution by marking it clearly, perhaps using a filled circle:
    
    ----|----|----|----|----|----|----|----|----|----|----|----|---->
    -1   0    1    2    3    4    5    6    7    8    9   10  
             ● 
           3/8

The filled circle means that 3/8 is included in the solution set.

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