Graph |x|<=3 |y|<=4

$| x | \leq 3$ $| y | \leq 4$

Step 1

Solve for $x$ .

Write $| x | \leq 3$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$x \geq 0$

In the piece where $x$ is non-negative, remove the absolute value.

$x \leq 3$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$x < 0$

In the piece where $x$ is negative, remove the absolute value and multiply by $- 1$ .

$- x \leq 3$

Write as a piecewise.

${\begin{cases} x \leq 3 & x \geq 0 \\ - x \leq 3 & x < 0 \end{cases}$

Find the intersection of $x \leq 3$ and $x \geq 0$ .

$0 \leq x \leq 3$

Solve $- x \leq 3$ when $x < 0$ .

Divide each term in $- x \leq 3$ by $- 1$ and simplify.

Divide each term in $- x \leq 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{3}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$x \geq - 3$

Find the intersection of $x \geq - 3$ and $x < 0$ .

$- 3 \leq x < 0$

Find the union of the solutions.

$- 3 \leq x \leq 3$

Step 2

Solve for $y$ .

Write $| y | \leq 4$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$y \geq 0$

In the piece where $y$ is non-negative, remove the absolute value.

$y \leq 4$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$y < 0$

In the piece where $y$ is negative, remove the absolute value and multiply by $- 1$ .

$- y \leq 4$

Write as a piecewise.

${\begin{cases} y \leq 4 & y \geq 0 \\ - y \leq 4 & y < 0 \end{cases}$

Find the intersection of $y \leq 4$ and $y \geq 0$ .

$0 \leq y \leq 4$

Solve $- y \leq 4$ when $y < 0$ .

Divide each term in $- y \leq 4$ by $- 1$ and simplify.

Divide each term in $- y \leq 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \geq \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} \geq \frac{4}{- 1}$

Divide $y$ by $1$ .

$y \geq \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$y \geq - 4$

Find the intersection of $y \geq - 4$ and $y < 0$ .

$- 4 \leq y < 0$

Find the union of the solutions.

$- 4 \leq y \leq 4$

Step 3

Plot each graph on the same coordinate system.

$| x | \leq 3$

$| y | \leq 4$

Step 4

Graph |x|<=3 |y|<=4

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