Solve for x -3<=(5x+17)/2<5

$- 3 \leq \frac{5 x + 17}{2} < 5$

Step 1

Multiply each term in the inequality by $2$ .

$- 3 \cdot 2 \leq \frac{5 x + 17}{2} \cdot 2 < 5 \cdot 2$

Step 2

Multiply $- 3$ by $2$ .

$- 6 \leq \frac{5 x + 17}{2} \cdot 2 < 5 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 6 \leq \frac{5 x + 17}{2} \cdot 2 < 5 \cdot 2$

Rewrite the expression.

$- 6 \leq 5 x + 17 < 5 \cdot 2$

Step 4

Multiply $5$ by $2$ .

$- 6 \leq 5 x + 17 < 10$

Step 5

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

Subtract $17$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 6 - 17 \leq 5 x < 10 - 17$

Subtract $17$ from $- 6$ .

$- 23 \leq 5 x < 10 - 17$

Subtract $17$ from $10$ .

$- 23 \leq 5 x < - 7$

Step 6

Divide each term in the inequality by $5$ .

$\frac{- 23}{5} \leq \frac{5 x}{5} < \frac{- 7}{5}$

Step 7

Move the negative in front of the fraction.

$- \frac{23}{5} \leq \frac{5 x}{5} < \frac{- 7}{5}$

Step 8

Cancel the common factor of $5$ .

Cancel the common factor.

$- \frac{23}{5} \leq \frac{5 x}{5} < \frac{- 7}{5}$

Divide $x$ by $1$ .

$- \frac{23}{5} \leq x < \frac{- 7}{5}$

Step 9

Move the negative in front of the fraction.

$- \frac{23}{5} \leq x < - \frac{7}{5}$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$- \frac{23}{5} \leq x < - \frac{7}{5}$

Interval Notation:

$[- \frac{23}{5}, - \frac{7}{5})$

Step 11

Solve for x -3<=(5x+17)/2<5

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