Finite Math Examples

$3 x + y < - 4$

Step 1

Subtract $y$ from both sides of the inequality.

$3 x < - 4 - y$

Step 2

Divide each term in $3 x < - 4 - y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x < - 4 - y$ by $3$ .

$\frac{3 x}{3} < \frac{- 4}{3} + \frac{- y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 4}{3} + \frac{- y}{3}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 4}{3} + \frac{- y}{3}$

$x < \frac{- 4}{3} + \frac{- y}{3}$

$x < \frac{- 4}{3} + \frac{- y}{3}$

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

Move the negative in front of the fraction.

$x < - \frac{4}{3} + \frac{- y}{3}$

Step 2.3.1.2

Move the negative in front of the fraction.

$x < - \frac{4}{3} - \frac{y}{3}$

$x < - \frac{4}{3} - \frac{y}{3}$

$x < - \frac{4}{3} - \frac{y}{3}$

$x < - \frac{4}{3} - \frac{y}{3}$

Step 3

Convert the inequality to interval notation.

$(- \infty, - \frac{4}{3} - \frac{y}{3})$

Step 4

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