Algebra Examples

$y \geq \sqrt{4 x + 8}$

Step 1

Simplify $\sqrt{4 x + 8}$ .

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Step 1.1

Factor $4$ out of $4 x + 8$ .

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Step 1.1.1

Factor $4$ out of $4 x$ .

$y \geq \sqrt{4 (x) + 8}$

Step 1.1.2

Factor $4$ out of $8$ .

$y \geq \sqrt{4 x + 4 \cdot 2}$

Step 1.1.3

Factor $4$ out of $4 x + 4 \cdot 2$ .

$y \geq \sqrt{4 (x + 2)}$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$y \geq \sqrt{2^{2} (x + 2)}$

Step 1.3

Pull terms out from under the radical.

$y \geq 2 \sqrt{x + 2}$

Step 2

The equation is not linear, so a constant slope does not exist.

Not Linear

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $2 \sqrt{x + 2}$ .

$y \geq 2 \sqrt{x + 2}$

Step 4