Solve for x -4+x<=2(x-5)

$- 4 + x \leq 2 (x - 5)$

Step 1

Simplify $2 (x - 5)$ .

Rewrite.

$- 4 + x \leq 0 + 0 + 2 (x - 5)$

Simplify by adding zeros.

$- 4 + x \leq 2 (x - 5)$

Apply the distributive property.

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

Multiply $2$ by $- 5$ .

$- 4 + x \leq 2 x - 10$

Step 2

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

Subtract $2 x$ from both sides of the inequality.

$- 4 + x - 2 x \leq - 10$

Subtract $2 x$ from $x$ .

$- 4 - x \leq - 10$

Step 3

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

Add $4$ to both sides of the inequality.

$- x \leq - 10 + 4$

Add $- 10$ and $4$ .

$- x \leq - 6$

Step 4

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x \geq 6$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 6$

Interval Notation:

$[6, \infty)$

Solve for x -4+x<=2(x-5)

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