Algebra Examples

$y < 13 \sqrt{9 x - 9} + 7$

Step 1

Simplify each term.

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Step 1.1

Factor $9$ out of $9 x - 9$ .

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Step 1.1.1

Factor $9$ out of $9 x$ .

$y < 13 \sqrt{9 (x) - 9} + 7$

Step 1.1.2

Factor $9$ out of $- 9$ .

$y < 13 \sqrt{9 (x) + 9 (- 1)} + 7$

Step 1.1.3

Factor $9$ out of $9 (x) + 9 (- 1)$ .

$y < 13 \sqrt{9 (x - 1)} + 7$

Step 1.2

Rewrite $9$ as $3^{2}$ .

$y < 13 \sqrt{3^{2} (x - 1)} + 7$

Step 1.3

Pull terms out from under the radical.

$y < 13 (3 \sqrt{x - 1}) + 7$

Step 1.4

Multiply $3$ by $13$ .

$y < 39 \sqrt{x - 1} + 7$

Step 2

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

Not Linear

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $39 \sqrt{x - 1} + 7$ .

$y < 39 \sqrt{x - 1} + 7$

Step 4