Graph |x|+5>=11

$| x | + 5 \geq 11$

Step 1

Write $| x | + 5 \geq 11$ 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.

$x + 5 \geq 11$

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 $- 1$ .

$- x + 5 \geq 11$

Write as a piecewise.

${\begin{cases} x + 5 \geq 11 & x \geq 0 \\ - x + 5 \geq 11 & x < 0 \end{cases}$

Step 2

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

Subtract $5$ from both sides of the inequality.

$x \geq 11 - 5$

Subtract $5$ from $11$ .

$x \geq 6$

Step 3

Solve $- x + 5 \geq 11$ for $x$ .

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

Subtract $5$ from both sides of the inequality.

$- x \geq 11 - 5$

Subtract $5$ from $11$ .

$- x \geq 6$

Divide each term in $- x \geq 6$ by $- 1$ and simplify.

Divide each term in $- x \geq 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{6}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{6}{- 1}$

Simplify the right side.

Divide $6$ by $- 1$ .

$x \leq - 6$

Step 4

Find the union of the solutions.

$x \leq - 6$ or $x \geq 6$

Step 5

Graph |x|+5>=11

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