Solve the Inequality for x 3-(x-6)<=4x-5

$3 - (x - 6) \leq 4 x - 5$

Simplify $3 - (x - 6)$ .

Simplify each term.

Apply the distributive property.

$3 - x - - 6 \leq 4 x - 5$

Multiply $- 1$ by $- 6$ .

$3 - x + 6 \leq 4 x - 5$

Add $3$ and $6$ .

$- x + 9 \leq 4 x - 5$

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

Subtract $4 x$ from both sides of the inequality.

$- x + 9 - 4 x \leq - 5$

Subtract $4 x$ from $- x$ .

$- 5 x + 9 \leq - 5$

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

Subtract $9$ from both sides of the inequality.

$- 5 x \leq - 5 - 9$

Subtract $9$ from $- 5$ .

$- 5 x \leq - 14$

Divide each term in $- 5 x \leq - 14$ by $- 5$ and simplify.

Divide each term in $- 5 x \leq - 14$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{- 14}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{- 14}{- 5}$

Divide $x$ by $1$ .

$x \geq \frac{- 14}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \geq \frac{14}{5}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{14}{5}$

Interval Notation:

$[\frac{14}{5}, \infty)$

Solve the Inequality for x 3-(x-6)<=4x-5

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