Question

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

Answer 1

Answer:

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

5. The negative case of this equation is x – 12 = –0.75.

Answer 2

we have  

$0.5-\left|x-12\right|=-0.25$  

we know that        

The absolute value has two solutions

Subtract  $0.5$ both sides

$-\left|x-12\right|=-0.25-0.5$  

$-\left|x-12\right|=-0.75$  

Step 1

Find the first solution (Case positive)

$-[+(x-12)]=-0.75$

$-x+12=-0.75$

Subtract  $12$ both sides

$-x+12-12=-0.75-12$

$-x=-12.75$

Multiply by $-1$ both sides

$x=12.75$

Step 2

Find the second solution (Case negative)

$-[-(x-12)]=-0.75$

$x-12=-0.75$

Adds  $12$ both sides

$x=-0.75+12$

$x=11.25$

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 $0.5-(x-12)=-0.25$ -----> 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