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).