Finite Math Examples

$- 17 < - 3 x + 1$

Step 1

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

$- 3 x + 1 > - 17$

Step 2

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

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Step 2.1

Subtract $1$ from both sides of the inequality.

$- 3 x > - 17 - 1$

Step 2.2

Subtract $1$ from $- 17$ .

$- 3 x > - 18$

Step 3

Divide each term in $- 3 x > - 18$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 x > - 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{- 18}{- 3}$

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.

$\frac{- 3 x}{- 3} < \frac{- 18}{- 3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 18}{- 3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 18$ by $- 3$ .

$x < 6$

Step 4

Convert the inequality to interval notation.

$(- \infty, 6)$

Step 5