Algebra Examples

$x + 12 < 8 - 3 x$

Step 1

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

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Step 1.1

Add $3 x$ to both sides of the inequality.

$x + 12 + 3 x < 8$

Step 1.2

Add $x$ and $3 x$ .

$4 x + 12 < 8$

Step 2

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

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Step 2.1

Subtract $12$ from both sides of the inequality.

$4 x < 8 - 12$

Step 2.2

Subtract $12$ from $8$ .

$4 x < - 4$

Step 3

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

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 4$ by $4$ .

$x < - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$