Solve the Inequality for x 3x<1/2(4x+4)

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

Step 1

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$3 x < 2 x + 2$

Step 2

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

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

$3 x - 2 x < 2$

Subtract $2 x$ from $3 x$ .

$x < 2$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$