Solve for x -5(x-4)>=2(1-x)

$- 5 (x - 4) \geq 2 (1 - x)$

Step 1

Simplify $- 5 (x - 4)$ .

Start simplifying.

$0 + 0 - 5 (x - 4) \geq 2 (1 - x)$

Simplify by adding zeros.

$- 5 (x - 4) \geq 2 (1 - x)$

Apply the distributive property.

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

Multiply $- 5$ by $- 4$ .

$- 5 x + 20 \geq 2 (1 - x)$

Step 2

Simplify $2 (1 - x)$ .

Apply the distributive property.

$- 5 x + 20 \geq 2 \cdot 1 + 2 (- x)$

Multiply.

Multiply $2$ by $1$ .

$- 5 x + 20 \geq 2 + 2 (- x)$

Multiply $- 1$ by $2$ .

$- 5 x + 20 \geq 2 - 2 x$

Step 3

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

Add $2 x$ to both sides of the inequality.

$- 5 x + 20 + 2 x \geq 2$

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

$- 3 x + 20 \geq 2$

Step 4

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

Subtract $20$ from both sides of the inequality.

$- 3 x \geq 2 - 20$

Subtract $20$ from $2$ .

$- 3 x \geq - 18$

Step 5

Divide each term in $- 3 x \geq - 18$ by $- 3$ and simplify.

Divide each term in $- 3 x \geq - 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \leq \frac{- 18}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \leq \frac{- 18}{- 3}$

Divide $x$ by $1$ .

$x \leq \frac{- 18}{- 3}$

Simplify the right side.

Divide $- 18$ by $- 3$ .

$x \leq 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq 6$

Interval Notation:

$(- \infty, 6]$

Solve for x -5(x-4)>=2(1-x)

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