Finite Math Examples

$3 x - 1 < 5 (x + 1)$

Step 1

Simplify $5 (x + 1)$ .

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Step 1.1

Rewrite.

$3 x - 1 < 0 + 0 + 5 (x + 1)$

Step 1.2

Simplify by adding zeros.

$3 x - 1 < 5 (x + 1)$

Step 1.3

Apply the distributive property.

$3 x - 1 < 5 x + 5 \cdot 1$

Step 1.4

Multiply $5$ by $1$ .

$3 x - 1 < 5 x + 5$

Step 2

Move all terms containing $x$ to the left side of the inequality.

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Step 2.1

Subtract $5 x$ from both sides of the inequality.

$3 x - 1 - 5 x < 5$

Step 2.2

Subtract $5 x$ from $3 x$ .

$- 2 x - 1 < 5$

Step 3

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

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Step 3.1

Add $1$ to both sides of the inequality.

$- 2 x < 5 + 1$

Step 3.2

Add $5$ and $1$ .

$- 2 x < 6$

Step 4

Divide each term in $- 2 x < 6$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 x < 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{6}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{6}{- 2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{6}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $6$ by $- 2$ .

$x > - 3$

Step 5

Convert the inequality to interval notation.

$(- 3, \infty)$

Step 6