Graph 6-2(x-4)<5(1-x)

$6 - 2 (x - 4) < 5 (1 - x)$

Step 1

Simplify $6 - 2 (x - 4)$ .

Simplify each term.

Apply the distributive property.

$6 - 2 x - 2 \cdot - 4 < 5 (1 - x)$

Multiply $- 2$ by $- 4$ .

$6 - 2 x + 8 < 5 (1 - x)$

Add $6$ and $8$ .

$- 2 x + 14 < 5 (1 - x)$

Step 2

Simplify $5 (1 - x)$ .

Apply the distributive property.

$- 2 x + 14 < 5 \cdot 1 + 5 (- x)$

Multiply.

Multiply $5$ by $1$ .

$- 2 x + 14 < 5 + 5 (- x)$

Multiply $- 1$ by $5$ .

$- 2 x + 14 < 5 - 5 x$

Step 3

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

Add $5 x$ to both sides of the inequality.

$- 2 x + 14 + 5 x < 5$

Add $- 2 x$ and $5 x$ .

$3 x + 14 < 5$

Step 4

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

Subtract $14$ from both sides of the inequality.

$3 x < 5 - 14$

Subtract $14$ from $5$ .

$3 x < - 9$

Step 5

Divide each term in $3 x < - 9$ by $3$ and simplify.

Divide each term in $3 x < - 9$ by $3$ .

$\frac{3 x}{3} < \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 9}{3}$

Divide $x$ by $1$ .

$x < \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$x < - 3$

Step 6