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Eddi Din [679]
2 years ago
7

Solve the equation.

Mathematics
1 answer:
lawyer [7]2 years ago
7 0

Answer:

  • x=12
  • x=9

Step-by-step explanation:

1) Eliminate parentheses:

  0.1x +18.8 = -4 +2x

  22.8 = 1.9x . . . . . . . . . add 4 - 0.1x

  12 = x . . . . . . . . . . . . . divide by 1.9

__

2) Eliminate parentheses:

  -16 +4x = 0.8x +12.8

  3.2x = 28.8 . . . . . . . . add 16 - 0.8x

  x = 9 . . . . . . . . . . . . . .divide by 3.2

_____

<em>Comments on the solutions</em>

The expression we add in each case eliminates the constant on one side of the equation and the variable term on the other side. That leaves an equation of the form ...

  variable term = constant

We choose to eliminate the smaller variable term (the one with the coefficient farthest to the left on the number line). Then the constant we eliminate is the on on the other side of the equation. This choice ensures that the remaining variable term has a positive coefficient, tending to reduce errors.

__

You can work these problems by methods that eliminate fractions. Here, the fractions are decimal values, so are not that difficult to deal with. In any event, it is good to be able to work with numbers in any form: fractions, decimals, integers. It can save some steps.

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Explanation:

This is a self-answering question: you solve it by graphing the equations.

<em>The solution is where the lines intersect</em>. The point of intersection of the lines is the point that satisfies all the equations for the lines, hence is a solution to the system. If they do not intersect, there are no solutions. If the lines are coincident, there are an infinite number of solutions.

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The equations can be graphed by any of a number of methods. (My favorite is to let a graphing calculator do it.) The method of choice depends on the coefficients and the form the equations are given in. Methods of graphing are a topic for a more lengthy discussion.

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