Question

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

Answer 1

Given expression:

• 
  `√(2x+2)+√(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]