Pre-Algebra Examples

$3 x + x < 2 x + 12$

Step 1

Add $3 x$ and $x$ .

$4 x < 2 x + 12$

Step 2

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

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Step 2.1

Subtract $2 x$ from both sides of the inequality.

$4 x - 2 x < 12$

Step 2.2

Subtract $2 x$ from $4 x$ .

$2 x < 12$

Step 3

Divide each term in $2 x < 12$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x < 12$ by $2$ .

$\frac{2 x}{2} < \frac{12}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} < \frac{12}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{12}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $12$ by $2$ .

$x < 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 6$

Interval Notation:

$(- \infty, 6)$