Solve for x -4(1-x)<5(x-2)

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

Step 1

Simplify $- 4 (1 - x)$ .

Rewrite.

$0 + 0 - 4 (1 - x) < 5 (x - 2)$

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $- 4$ by $1$ .

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

Multiply $- 1$ by $- 4$ .

$- 4 + 4 x < 5 (x - 2)$

Step 2

Simplify $5 (x - 2)$ .

Apply the distributive property.

$- 4 + 4 x < 5 x + 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$- 4 + 4 x < 5 x - 10$

Step 3

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

Subtract $5 x$ from both sides of the inequality.

$- 4 + 4 x - 5 x < - 10$

Subtract $5 x$ from $4 x$ .

$- 4 - x < - 10$

Step 4

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

Add $4$ to both sides of the inequality.

$- x < - 10 + 4$

Add $- 10$ and $4$ .

$- x < - 6$

Step 5

Divide each term in $- x < - 6$ by $- 1$ and simplify.

Divide each term in $- x < - 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x > \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x > 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 6$

Interval Notation:

$(6, \infty)$

Solve for x -4(1-x)<5(x-2)

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