Solve the Inequality for x -8<=-(x-6/5)-6

$- 8 \leq - (x - \frac{6}{5}) - 6$

Step 1

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

$- (x - \frac{6}{5}) - 6 \geq - 8$

Step 2

Simplify $- (x - \frac{6}{5}) - 6$ .

Simplify each term.

Apply the distributive property.

$- x - - \frac{6}{5} - 6 \geq - 8$

Multiply $- - \frac{6}{5}$ .

Multiply $- 1$ by $- 1$ .

$- x + 1 (\frac{6}{5}) - 6 \geq - 8$

Multiply $\frac{6}{5}$ by $1$ .

$- x + \frac{6}{5} - 6 \geq - 8$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- x + \frac{6}{5} - 6 \cdot \frac{5}{5} \geq - 8$

Combine $- 6$ and $\frac{5}{5}$ .

$- x + \frac{6}{5} + \frac{- 6 \cdot 5}{5} \geq - 8$

Combine the numerators over the common denominator.

$- x + \frac{6 - 6 \cdot 5}{5} \geq - 8$

Simplify the numerator.

Multiply $- 6$ by $5$ .

$- x + \frac{6 - 30}{5} \geq - 8$

Subtract $30$ from $6$ .

$- x + \frac{- 24}{5} \geq - 8$

Move the negative in front of the fraction.

$- x - \frac{24}{5} \geq - 8$

Step 3

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

Add $\frac{24}{5}$ to both sides of the inequality.

$- x \geq - 8 + \frac{24}{5}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- x \geq - 8 \cdot \frac{5}{5} + \frac{24}{5}$

Combine $- 8$ and $\frac{5}{5}$ .

$- x \geq \frac{- 8 \cdot 5}{5} + \frac{24}{5}$

Combine the numerators over the common denominator.

$- x \geq \frac{- 8 \cdot 5 + 24}{5}$

Simplify the numerator.

Multiply $- 8$ by $5$ .

$- x \geq \frac{- 40 + 24}{5}$

Add $- 40$ and $24$ .

$- x \geq \frac{- 16}{5}$

Move the negative in front of the fraction.

$- x \geq - \frac{16}{5}$

Step 4

Divide each term in $- x \geq - \frac{16}{5}$ by $- 1$ and simplify.

Divide each term in $- x \geq - \frac{16}{5}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- \frac{16}{5}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- \frac{16}{5}}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{- \frac{16}{5}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x \leq \frac{\frac{16}{5}}{1}$

Divide $\frac{16}{5}$ by $1$ .

$x \leq \frac{16}{5}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{16}{5}$

Interval Notation:

$(- \infty, \frac{16}{5}]$

Solve the Inequality for x -8<=-(x-6/5)-6

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