How many solutions can be found for the equation 0.75x + 40 + 0.35x + 20 + 0.35x + 20?

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To determine how many solutions exist for the equation 0.75x + 40 + 0.35x + 20 + 0.35x + 20 = 0, we can start by simplifying the equation step-by-step.

First, let’s combine like terms. The terms involving x are:

  • 0.75x
  • 0.35x
  • 0.35x

Now, we can add these together:

0.75x + 0.35x + 0.35x = 0.75x + 0.7x = 1.45x

Next, let’s add the constant terms:

  • 40
  • 20
  • 20

40 + 20 + 20 = 80

Now, we can rewrite the equation as:

1.45x + 80 = 0

To find x, we isolate it:

  1. Subtract 80 from both sides:
  2. 1.45x = -80
  3. Now divide both sides by 1.45:
  4. x = - rac{80}{1.45}

This equation yields a single value of x, which means that there is exactly one solution to the equation.

In summary, the equation 0.75x + 40 + 0.35x + 20 + 0.35x + 20 = 0 has one solution. This is a linear equation since it can be expressed in the form Ax + B = 0. Linear equations provide one solution, as they represent a straight line on a graph intersecting the x-axis at exactly one point.

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