Algebra Examples

$3 x < 6 (x - 1) - 12$

Step 1

Simplify $6 (x - 1) - 12$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 x < 6 x + 6 \cdot - 1 - 12$

Step 1.1.2

Multiply $6$ by $- 1$ .

$3 x < 6 x - 6 - 12$

Step 1.2

Subtract $12$ from $- 6$ .

$3 x < 6 x - 18$

Step 2

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

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Step 2.1

Subtract $6 x$ from both sides of the inequality.

$3 x - 6 x < - 18$

Step 2.2

Subtract $6 x$ from $3 x$ .

$- 3 x < - 18$

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

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$