Algebra Examples

$3 x < \frac{1}{2} (4 x + 4)$

Step 1

Simplify $\frac{1}{2} \cdot (4 x + 4)$ .

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Step 1.1

Apply the distributive property.

$3 x < \frac{1}{2} (4 x) + \frac{1}{2} \cdot 4$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4 x$ .

$3 x < \frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot 4$

Step 1.2.2

Cancel the common factor.

$3 x < \frac{1}{2} (2 (2 x)) + \frac{1}{2} \cdot 4$

Step 1.2.3

Rewrite the expression.

$3 x < 2 x + \frac{1}{2} \cdot 4$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$3 x < 2 x + \frac{1}{2} \cdot (2 (2))$

Step 1.3.2

Cancel the common factor.

$3 x < 2 x + \frac{1}{2} \cdot (2 \cdot 2)$

Step 1.3.3

Rewrite the expression.

$3 x < 2 x + 2$

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.

$3 x - 2 x < 2$

Step 2.2

Subtract $2 x$ from $3 x$ .

$x < 2$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$