Algebra Examples

$3 - y \geq - | x - 4 |$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $3$ from both sides of the inequality.

$- y \geq - | x - 4 | - 3$

Step 1.2

Divide each term in $- y \geq - | x - 4 | - 3$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- y \geq - | x - 4 | - 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \leq \frac{- | x - 4 |}{- 1} + \frac{- 3}{- 1}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} \leq \frac{- | x - 4 |}{- 1} + \frac{- 3}{- 1}$

Step 1.2.2.2

Divide $y$ by $1$ .

$y \leq \frac{- | x - 4 |}{- 1} + \frac{- 3}{- 1}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Dividing two negative values results in a positive value.

$y \leq \frac{| x - 4 |}{1} + \frac{- 3}{- 1}$

Step 1.2.3.1.2

Divide $| x - 4 |$ by $1$ .

$y \leq | x - 4 | + \frac{- 3}{- 1}$

Step 1.2.3.1.3

Divide $- 3$ by $- 1$ .

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

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 $| x - 4 | + 3$ .

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

Step 4