Solve for x -2<=(5-x)/3<=2

$- 2 \leq \frac{5 - x}{3} \leq 2$

Step 1

Multiply each term in the inequality by $3$ .

$- 2 \cdot 3 \leq \frac{5 - x}{3} \cdot 3 \leq 2 \cdot 3$

Step 2

Multiply $- 2$ by $3$ .

$- 6 \leq \frac{5 - x}{3} \cdot 3 \leq 2 \cdot 3$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$- 6 \leq \frac{5 - x}{3} \cdot 3 \leq 2 \cdot 3$

Rewrite the expression.

$- 6 \leq 5 - x \leq 2 \cdot 3$

Step 4

Multiply $2$ by $3$ .

$- 6 \leq 5 - x \leq 6$

Step 5

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 5 \leq - x \leq 6 - 5$

Subtract $5$ from $- 6$ .

$- 11 \leq - x \leq 6 - 5$

Subtract $5$ from $6$ .

$- 11 \leq - x \leq 1$

Step 6

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

$\frac{- 11}{- 1} \geq \frac{- x}{- 1} \geq \frac{1}{- 1}$

Step 7

Divide $- 11$ by $- 1$ .

$11 \geq \frac{- x}{- 1} \geq \frac{1}{- 1}$

Step 8

Dividing two negative values results in a positive value.

$11 \geq \frac{x}{1} \geq \frac{1}{- 1}$

Step 9

Divide $x$ by $1$ .

$11 \geq x \geq \frac{1}{- 1}$

Step 10

Divide $1$ by $- 1$ .

$11 \geq x \geq - 1$

Step 11

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 1 \leq x \leq 11$

Step 12

The result can be shown in multiple forms.

Inequality Form:

$- 1 \leq x \leq 11$

Interval Notation:

$[- 1, 11]$

Step 13

Solve for x -2<=(5-x)/3<=2

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