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

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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