Finite Math Examples

$78 < 6 - 3 x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$6 - 3 x > 78$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the inequality.

$- 3 x > 78 - 6$

Step 2.2

Subtract $6$ from $78$ .

$- 3 x > 72$

Step 3

Divide each term in $- 3 x > 72$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 x > 72$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{72}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{72}{- 3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{72}{- 3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $72$ by $- 3$ .

$x < - 24$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 24$

Interval Notation:

$(- \infty, - 24)$