Solve the Inequality for x 9x-8<=-2x-6(-x+2/3)

$9 x - 8 \leq - 2 x - 6 (- x + \frac{2}{3})$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- 2 x - 6 (- x + \frac{2}{3}) \geq 9 x - 8$

Step 2

Simplify $- 2 x - 6 (- x + \frac{2}{3})$ .

Simplify each term.

Apply the distributive property.

$- 2 x - 6 (- x) - 6 (\frac{2}{3}) \geq 9 x - 8$

Multiply $- 1$ by $- 6$ .

$- 2 x + 6 x - 6 (\frac{2}{3}) \geq 9 x - 8$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$- 2 x + 6 x + 3 (- 2) \frac{2}{3} \geq 9 x - 8$

Cancel the common factor.

$- 2 x + 6 x + 3 \cdot - 2 \frac{2}{3} \geq 9 x - 8$

Rewrite the expression.

$- 2 x + 6 x - 2 \cdot 2 \geq 9 x - 8$

Multiply $- 2$ by $2$ .

$- 2 x + 6 x - 4 \geq 9 x - 8$

Add $- 2 x$ and $6 x$ .

$4 x - 4 \geq 9 x - 8$

Step 3

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

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

$4 x - 4 - 9 x \geq - 8$

Subtract $9 x$ from $4 x$ .

$- 5 x - 4 \geq - 8$

Step 4

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

Add $4$ to both sides of the inequality.

$- 5 x \geq - 8 + 4$

Add $- 8$ and $4$ .

$- 5 x \geq - 4$

Step 5

Divide each term in $- 5 x \geq - 4$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq - 4$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 4}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 4}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{- 4}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{4}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{4}{5}$

Interval Notation:

$(- \infty, \frac{4}{5}]$

Solve the Inequality for x 9x-8<=-2x-6(-x+2/3)

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