Solve the Inequality for x -3(x-4)>6(x-1)

$- 3 (x - 4) > 6 (x - 1)$

Step 1

Simplify $- 3 (x - 4)$ .

Start simplifying.

$0 + 0 - 3 (x - 4) > 6 (x - 1)$

Simplify by adding zeros.

$- 3 (x - 4) > 6 (x - 1)$

Apply the distributive property.

$- 3 x - 3 \cdot - 4 > 6 (x - 1)$

Multiply $- 3$ by $- 4$ .

$- 3 x + 12 > 6 (x - 1)$

Step 2

Simplify $6 (x - 1)$ .

Apply the distributive property.

$- 3 x + 12 > 6 x + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

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

Step 3

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

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

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

Subtract $6 x$ from $- 3 x$ .

$- 9 x + 12 > - 6$

Step 4

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

Subtract $12$ from both sides of the inequality.

$- 9 x > - 6 - 12$

Subtract $12$ from $- 6$ .

$- 9 x > - 18$

Step 5

Divide each term in $- 9 x > - 18$ by $- 9$ and simplify.

Divide each term in $- 9 x > - 18$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} < \frac{- 18}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} < \frac{- 18}{- 9}$

Divide $x$ by $1$ .

$x < \frac{- 18}{- 9}$

Simplify the right side.

Divide $- 18$ by $- 9$ .

$x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Solve the Inequality for x -3(x-4)>6(x-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.