Solve the Inequality for x 2(x-3)+5x<=9x-14

$2 (x - 3) + 5 x \leq 9 x - 14$

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

Simplify each term.

Apply the distributive property.

$2 x + 2 \cdot - 3 + 5 x \leq 9 x - 14$

Multiply $2$ by $- 3$ .

$2 x - 6 + 5 x \leq 9 x - 14$

Add $2 x$ and $5 x$ .

$7 x - 6 \leq 9 x - 14$

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

Subtract $9 x$ from both sides of the inequality.

$7 x - 6 - 9 x \leq - 14$

Subtract $9 x$ from $7 x$ .

$- 2 x - 6 \leq - 14$

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

Add $6$ to both sides of the inequality.

$- 2 x \leq - 14 + 6$

Add $- 14$ and $6$ .

$- 2 x \leq - 8$

Divide each term in $- 2 x \leq - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq - 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x \geq 4$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 4$

Interval Notation:

$[4, \infty)$

Solve the Inequality for x 2(x-3)+5x<=9x-14

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