Algebra Examples

$y + 2 \leq | \frac{1}{2} x |$

Step 1

Solve for $y$ .

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Step 1.1

Simplify $| \frac{1}{2} x |$ .

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Step 1.1.1

Rewrite.

$y + 2 \leq 0 + 0 + | \frac{1}{2} x |$

Step 1.1.2

Simplify by adding zeros.

$y + 2 \leq | \frac{1}{2} x |$

Step 1.1.3

Combine $\frac{1}{2}$ and $x$ .

$y + 2 \leq | \frac{x}{2} |$

Step 1.1.4

Remove non-negative terms from the absolute value.

$y + 2 \leq \frac{| x |}{2}$

Step 1.2

Subtract $2$ from both sides of the inequality.

$y \leq \frac{| x |}{2} - 2$

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 below the boundary line since $y$ is less than $\frac{| x |}{2} - 2$ .

$y \leq \frac{| x |}{2} - 2$

Step 4