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Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.

The equation will have no solutions.
A good first step for solving the equation is to subtract 0.5 from both sides of the equation.
A good first step for solving the equation is to split it into a positive case and a negative case.
The positive case of this equation is 0.5 – |x – 12| = 0.25.
The negative case of this equation is x – 12 = –0.75.
The equation will have only 1 solution

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facundo3141592

The true statement is:

"A good first step for solving the equation is to subtract 0.5 from both sides of the equation."

Which statements are true for solving the equation?

We have the absolute value equation:

0.5 - |x - 12| = 0.25

Now, if we subtract 0.5 from both sides, we get:

-|x - 12| = 0.25 - 0.5 = -0.25

Now we can multiply both sides by -1 to get:

|x - 12| = 0.25

Now we need to split in the negative and positive parts:

x - 12 = 0.25

x - 12 = -0.25

And now we can solve these two to get the two solutions:

  • x = 0.25 + 12 = 12.25
  • x = -0.25 +12 = 11.75

Now that we performed the whole solution, the statement that is true is:

"A good first step for solving the equation is to subtract 0.5 from both sides of the equation."

Al the other ones are false.

If you want to learn more about absolute value equations:

https://brainly.com/question/1622683

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smithcasperp

Answer:

For edge the answer is b and e

Step-by-step explanation:

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