Solve the Inequality for x 16>=-x+6>5

$16 \geq - x + 6 > 5$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $6$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$16 - 6 \geq - x > 5 - 6$

Subtract $6$ from $16$ .

$10 \geq - x > 5 - 6$

Subtract $6$ from $5$ .

$10 \geq - x > - 1$

Step 2

Multiply each term in the inequality by $- 1$ .

$\frac{10}{- 1} \leq \frac{- x}{- 1} < \frac{- 1}{- 1}$

Step 3

Divide $10$ by $- 1$ .

$- 10 \leq \frac{- x}{- 1} < \frac{- 1}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$- 10 \leq \frac{x}{1} < \frac{- 1}{- 1}$

Step 5

Divide $x$ by $1$ .

$- 10 \leq x < \frac{- 1}{- 1}$

Step 6

Divide $- 1$ by $- 1$ .

$- 10 \leq x < 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 10 \leq x < 1$

Interval Notation:

$[- 10, 1)$

Step 8