Solve the Inequality for x 3(x-2)<3-2(2x-6)

$3 (x - 2) < 3 - 2 (2 x - 6)$

Simplify $3 (x - 2)$ .

Rewrite.

$0 + 0 + 3 (x - 2) < 3 - 2 (2 x - 6)$

Simplify by adding zeros.

$3 (x - 2) < 3 - 2 (2 x - 6)$

Apply the distributive property.

$3 x + 3 \cdot - 2 < 3 - 2 (2 x - 6)$

Multiply $3$ by $- 2$ .

$3 x - 6 < 3 - 2 (2 x - 6)$

Simplify $3 - 2 (2 x - 6)$ .

Simplify each term.

Apply the distributive property.

$3 x - 6 < 3 - 2 (2 x) - 2 \cdot - 6$

Multiply $2$ by $- 2$ .

$3 x - 6 < 3 - 4 x - 2 \cdot - 6$

Multiply $- 2$ by $- 6$ .

$3 x - 6 < 3 - 4 x + 12$

Add $3$ and $12$ .

$3 x - 6 < - 4 x + 15$

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

Add $4 x$ to both sides of the inequality.

$3 x - 6 + 4 x < 15$

Add $3 x$ and $4 x$ .

$7 x - 6 < 15$

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

Add $6$ to both sides of the inequality.

$7 x < 15 + 6$

Add $15$ and $6$ .

$7 x < 21$

Divide each term in $7 x < 21$ by $7$ and simplify.

Divide each term in $7 x < 21$ by $7$ .

$\frac{7 x}{7} < \frac{21}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} < \frac{21}{7}$

Divide $x$ by $1$ .

$x < \frac{21}{7}$

Simplify the right side.

Divide $21$ by $7$ .

$x < 3$

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$

Solve the Inequality for x 3(x-2)<3-2(2x-6)

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