Problem 14 - Elementary Algebra

Question

Write the proper restrictions that must be placed on the variable so that each expression represents a real number. $$ \sqrt{x+5} $$

Step-by-Step Solution

Answer

Answer: The domain of the square root expression $$\sqrt{x+5}$$ is $$x \geq -5$$. This means the expression represents a real number for every x value greater than or equal to -5.

Step 1: Rewrite the inequality

To find the restrictions on the variable x, we first need to rewrite the inequality involving the expression inside the square root: $$ x + 5 \geq 0 $$

Step 2: Solve the inequality

In this step, we will solve the inequality by isolating x: \begin{align*} x + 5 &\geq 0 \\ x &\geq -5 \end{align*}

Step 3: Write the restrictions of the variable x

The inequality we found tells us the proper restrictions on the variable x for the expression to represent a real number: $$ x \geq -5 $$ The expression $$\sqrt{x+5}$$ represents a real number for every x value greater than or equal to -5.