Question

Indicate all possible values for the variable in each of the expressions: sqrt(2x+2)+sqrt(6-4x)

Answer 1

Answer:

Given expression:

• $\sqrt{2x+2}+\sqrt{6-4x}$

The first root is valid when:

• 2x + 2 ≥ 0 ⇒ 2x ≥ - 2 ⇒ x ≥ - 1

The second root is valid when:

• 6 - 4x ≥ 0 ⇒ 4x ≤ 6 ⇒ x ≤ 1.5

So the variable x can get values within interval:

• -1 ≤ x ≤ 1.5 or
• x = [-1, 1.5]