Match each term with the appropriate example 1. absolute value 2. all real numbers 3. x = -5 4. no solution 5. adding the opposite to both sides of the equation. a. |2x| = -10 b. 3x = 3x c. 5x = -25 d. | - 7| = 7 e. canceling

1.   Absolute value :  d.  | - 7| = 7

2.  All real numbers :  b.  3x = 3x

3.  x = -5  : c.  5x = -25

4.  No solution : a.  |2x| = -10

5.  Adding the opposite to both sides of the equation. : e.  Canceling

Step-by-step explanation:

1.   Absolute value :  d.  | - 7| = 7

The absolute value is considered the distance to 0... so if there's a negative sign in the value, the negative sign disappears.

2.  All real numbers :  b.  3x = 3x

If we divide both sides by 3, we have x = x, which will always be true.

3.  x = -5  : c.  5x = -25

If we multiply each side by 5, we have 5(x) = 5(-5) thus 5x = -25

4.  No solution : a.  |2x| = -10

The result of an absolute value cannot be a negative number.  So, that has no solution since there's no value of x that would make this true.

5.  Adding the opposite to both sides of the equation. : e.  Canceling

If you have for example (x = -5) and you add 5 on both sides, you cancel the value on the right side... (becomes x + 5 = 0).