Solve the Inequality for x 3(4-6x)>6x

$3 (4 - 6 x) > 6 x$

Step 1

Simplify $3 (4 - 6 x)$ .

Start simplifying.

$0 + 0 + 3 (4 - 6 x) > 6 x$

Simplify by adding zeros.

$3 (4 - 6 x) > 6 x$

Apply the distributive property.

$3 \cdot 4 + 3 (- 6 x) > 6 x$

Multiply.

Multiply $3$ by $4$ .

$12 + 3 (- 6 x) > 6 x$

Multiply $- 6$ by $3$ .

$12 - 18 x > 6 x$

Step 2

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

Subtract $6 x$ from both sides of the inequality.

$12 - 18 x - 6 x > 0$

Subtract $6 x$ from $- 18 x$ .

$12 - 24 x > 0$

Step 3

Subtract $12$ from both sides of the inequality.

$- 24 x > - 12$

Step 4

Divide each term in $- 24 x > - 12$ by $- 24$ and simplify.

Divide each term in $- 24 x > - 12$ by $- 24$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 24 x}{- 24} < \frac{- 12}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} < \frac{- 12}{- 24}$

Divide $x$ by $1$ .

$x < \frac{- 12}{- 24}$

Simplify the right side.

Cancel the common factor of $- 12$ and $- 24$ .

Factor $- 12$ out of $- 12$ .

$x < \frac{- 12 (1)}{- 24}$

Cancel the common factors.

Factor $- 12$ out of $- 24$ .

$x < \frac{- 12 \cdot 1}{- 12 \cdot 2}$

Cancel the common factor.

$x < \frac{- 12 \cdot 1}{- 12 \cdot 2}$

Rewrite the expression.

$x < \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{1}{2}$

Interval Notation:

$(- \infty, \frac{1}{2})$

Solve the Inequality for x 3(4-6x)>6x

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