Graph 5-x<2(x-3)+5

$5 - x < 2 (x - 3) + 5$

Step 1

Simplify $2 (x - 3) + 5$ .

Simplify each term.

Apply the distributive property.

$5 - x < 2 x + 2 \cdot - 3 + 5$

Multiply $2$ by $- 3$ .

$5 - x < 2 x - 6 + 5$

Add $- 6$ and $5$ .

$5 - x < 2 x - 1$

Step 2

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

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

$5 - x - 2 x < - 1$

Subtract $2 x$ from $- x$ .

$5 - 3 x < - 1$

Step 3

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

Subtract $5$ from both sides of the inequality.

$- 3 x < - 1 - 5$

Subtract $5$ from $- 1$ .

$- 3 x < - 6$

Step 4

Divide each term in $- 3 x < - 6$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{- 6}{- 3}$

Divide $x$ by $1$ .

$x > \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x > 2$

Step 5

Graph 5-x<2(x-3)+5

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