Algebra Examples

$y + 3 \leq | 3 x | - 1$

Step 1

Solve for $y$ .

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Step 1.1

Remove non-negative terms from the absolute value.

$y + 3 \leq 3 | x | - 1$

Step 1.2

Move all terms not containing $y$ to the right side of the inequality.

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Step 1.2.1

Subtract $3$ from both sides of the inequality.

$y \leq 3 | x | - 1 - 3$

Step 1.2.2

Subtract $3$ from $- 1$ .

$y \leq 3 | x | - 4$

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 below the boundary line since $y$ is less than $3 | x | - 4$ .

$y \leq 3 | x | - 4$

Step 4