Solve the Inequality for x -3(x-3)<=5(1-x)

$- 3 (x - 3) \leq 5 (1 - x)$

Step 1

Simplify $- 3 (x - 3)$ .

Start simplifying.

$0 + 0 - 3 (x - 3) \leq 5 (1 - x)$

Simplify by adding zeros.

$- 3 (x - 3) \leq 5 (1 - x)$

Apply the distributive property.

$- 3 x - 3 \cdot - 3 \leq 5 (1 - x)$

Multiply $- 3$ by $- 3$ .

$- 3 x + 9 \leq 5 (1 - x)$

Step 2

Simplify $5 (1 - x)$ .

Apply the distributive property.

$- 3 x + 9 \leq 5 \cdot 1 + 5 (- x)$

Multiply.

Multiply $5$ by $1$ .

$- 3 x + 9 \leq 5 + 5 (- x)$

Multiply $- 1$ by $5$ .

$- 3 x + 9 \leq 5 - 5 x$

Step 3

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

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

$- 3 x + 9 + 5 x \leq 5$

Add $- 3 x$ and $5 x$ .

$2 x + 9 \leq 5$

Step 4

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

Subtract $9$ from both sides of the inequality.

$2 x \leq 5 - 9$

Subtract $9$ from $5$ .

$2 x \leq - 4$

Step 5

Divide each term in $2 x \leq - 4$ by $2$ and simplify.

Divide each term in $2 x \leq - 4$ by $2$ .

$\frac{2 x}{2} \leq \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{- 4}{2}$

Divide $x$ by $1$ .

$x \leq \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$x \leq - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 2$

Interval Notation:

$(- \infty, - 2]$

Solve the Inequality for x -3(x-3)<=5(1-x)

Related Questions

Support LCMGCF.com by disabling your adblocker.