Finite Math Examples

$2 x + y \leq 10$

Step 1

Subtract $y$ from both sides of the inequality.

$2 x \leq 10 - y$

Step 2

Divide each term in $2 x \leq 10 - y$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x \leq 10 - y$ by $2$ .

$\frac{2 x}{2} \leq \frac{10}{2} + \frac{- y}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{10}{2} + \frac{- y}{2}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{10}{2} + \frac{- y}{2}$

$x \leq \frac{10}{2} + \frac{- y}{2}$

$x \leq \frac{10}{2} + \frac{- y}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $10$ by $2$ .

$x \leq 5 + \frac{- y}{2}$

Step 2.3.1.2

Move the negative in front of the fraction.

$x \leq 5 - \frac{y}{2}$

$x \leq 5 - \frac{y}{2}$

$x \leq 5 - \frac{y}{2}$

$x \leq 5 - \frac{y}{2}$

Step 3

Convert the inequality to interval notation.

$(- \infty, 5 - \frac{y}{2}]$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$