Solve for x -6.5<=(7x+6)/2<=20.5

$- 6.5 \leq \frac{7 x + 6}{2} \leq 20.5$

Step 1

Multiply each term in the inequality by $2$ .

$- 6.5 \cdot 2 \leq \frac{7 x + 6}{2} \cdot 2 \leq 20.5 \cdot 2$

Step 2

Multiply $- 6.5$ by $2$ .

$- 13 \leq \frac{7 x + 6}{2} \cdot 2 \leq 20.5 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 13 \leq \frac{7 x + 6}{2} \cdot 2 \leq 20.5 \cdot 2$

Rewrite the expression.

$- 13 \leq 7 x + 6 \leq 20.5 \cdot 2$

Step 4

Multiply $20.5$ by $2$ .

$- 13 \leq 7 x + 6 \leq 41$

Step 5

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.

$- 13 - 6 \leq 7 x \leq 41 - 6$

Subtract $6$ from $- 13$ .

$- 19 \leq 7 x \leq 41 - 6$

Subtract $6$ from $41$ .

$- 19 \leq 7 x \leq 35$

Step 6

Divide each term in the inequality by $7$ .

$\frac{- 19}{7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Step 7

Cancel the common factor of $- 19$ and $7$ .

Rewrite $- 19$ as $1 (- 19)$ .

$\frac{1 (- 19)}{7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Cancel the common factors.

Rewrite $7$ as $1 (7)$ .

$\frac{1 \cdot - 19}{1 \cdot 7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Cancel the common factor.

$\frac{1 \cdot - 19}{1 \cdot 7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Rewrite the expression.

$\frac{- 19}{7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Step 8

Move the negative in front of the fraction.

$- \frac{19}{7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Step 9

Cancel the common factor of $7$ .

Cancel the common factor.

$- \frac{19}{7} \leq \frac{7 x}{7} \leq \frac{35}{7}$

Divide $x$ by $1$ .

$- \frac{19}{7} \leq x \leq \frac{35}{7}$

Step 10

Divide $35$ by $7$ .

$- \frac{19}{7} \leq x \leq 5$

Step 11

The result can be shown in multiple forms.

Inequality Form:

$- \frac{19}{7} \leq x \leq 5$

Interval Notation:

$[- \frac{19}{7}, 5]$

Step 12

Solve for x -6.5<=(7x+6)/2<=20.5

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