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

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

Step 1

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

Start simplifying.

$0 + 0 - 3 (2 x - 5) < 5 (2 - x)$

Simplify by adding zeros.

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

Apply the distributive property.

$- 3 (2 x) - 3 \cdot - 5 < 5 (2 - x)$

Multiply.

Multiply $2$ by $- 3$ .

$- 6 x - 3 \cdot - 5 < 5 (2 - x)$

Multiply $- 3$ by $- 5$ .

$- 6 x + 15 < 5 (2 - x)$

Step 2

Simplify $5 (2 - x)$ .

Apply the distributive property.

$- 6 x + 15 < 5 \cdot 2 + 5 (- x)$

Multiply.

Multiply $5$ by $2$ .

$- 6 x + 15 < 10 + 5 (- x)$

Multiply $- 1$ by $5$ .

$- 6 x + 15 < 10 - 5 x$

Step 3

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

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

$- 6 x + 15 + 5 x < 10$

Add $- 6 x$ and $5 x$ .

$- x + 15 < 10$

Step 4

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

Subtract $15$ from both sides of the inequality.

$- x < 10 - 15$

Subtract $15$ from $10$ .

$- x < - 5$

Step 5

Divide each term in $- x < - 5$ by $- 1$ and simplify.

Divide each term in $- x < - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x > \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x > 5$

Step 6

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

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