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

we have  

we know that        

The absolute value has two solutions

Subtract   both sides

Step 1

Find the first solution (Case positive)

Subtract   both sides

Multiply by both sides

Step 2

Find the second solution (Case negative)

Adds   both sides

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 -----> 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

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.