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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

Respuesta :

calculista

we have  

[tex]0.5-\left|x-12\right|=-0.25[/tex]  

we know that        

The absolute value has two solutions

Subtract  [tex]0.5[/tex] both sides

[tex]-\left|x-12\right|=-0.25-0.5[/tex]  

[tex]-\left|x-12\right|=-0.75[/tex]  

Step 1

Find the first solution (Case positive)

[tex]-[+(x-12)]=-0.75[/tex]

[tex]-x+12=-0.75[/tex]

Subtract  [tex]12[/tex] both sides

[tex]-x+12-12=-0.75-12[/tex]

[tex]-x=-12.75[/tex]

Multiply by [tex]-1[/tex] both sides

[tex]x=12.75[/tex]

Step 2

Find the second solution (Case negative)

[tex]-[-(x-12)]=-0.75[/tex]

[tex]x-12=-0.75[/tex]

Adds  [tex]12[/tex] both sides

[tex]x=-0.75+12[/tex]

[tex]x=11.25[/tex]

Statements

case A) The equation will have no solutions

The statement is False

Because the equation has two solutions------> See the procedure

case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation

The statement is True ----->  See the procedure

case C) A good first step for solving the equation is to split it into a positive case and a negative case

The statement is False ----->  See the procedure

case D) The positive case of this equation is 0.5 – |x – 12| = 0.25

The statement is False

Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure

case E) The negative case of this equation is x – 12 = –0.75

The statement is True -----> see the procedure

case F) The equation will have only 1 solution

The statement is False

Because The equation has two solutions------> See the procedure


abidemiokin
  • 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.

Modulus equations and functions

Given the modulus expression given as:

0.5 – |x – 12| = –0.25

The modulus function shows that the equation will have 2 solutions (for the negative function and positive function)

Hence 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.

Learn more on inequality here: https://brainly.com/question/24372553

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