Solve for x -3(x-4)<=9+x

$- 3 (x - 4) \leq 9 + x$

Step 1

Simplify $- 3 (x - 4)$ .

Rewrite.

$0 + 0 - 3 (x - 4) \leq 9 + x$

Simplify by adding zeros.

$- 3 (x - 4) \leq 9 + x$

Apply the distributive property.

$- 3 x - 3 \cdot - 4 \leq 9 + x$

Multiply $- 3$ by $- 4$ .

$- 3 x + 12 \leq 9 + x$

Step 2

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

Subtract $x$ from both sides of the inequality.

$- 3 x + 12 - x \leq 9$

Subtract $x$ from $- 3 x$ .

$- 4 x + 12 \leq 9$

Step 3

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

Subtract $12$ from both sides of the inequality.

$- 4 x \leq 9 - 12$

Subtract $12$ from $9$ .

$- 4 x \leq - 3$

Step 4

Divide each term in $- 4 x \leq - 3$ by $- 4$ and simplify.

Divide each term in $- 4 x \leq - 3$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \geq \frac{- 3}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \geq \frac{- 3}{- 4}$

Divide $x$ by $1$ .

$x \geq \frac{- 3}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \geq \frac{3}{4}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{3}{4}$

Interval Notation:

$[\frac{3}{4}, \infty)$

Solve for x -3(x-4)<=9+x

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