Solve for x -9<=(4x+17)/3<7

$- 9 \leq \frac{4 x + 17}{3} < 7$

Step 1

Multiply each term in the inequality by $3$ .

$- 9 \cdot 3 \leq \frac{4 x + 17}{3} \cdot 3 < 7 \cdot 3$

Step 2

Multiply $- 9$ by $3$ .

$- 27 \leq \frac{4 x + 17}{3} \cdot 3 < 7 \cdot 3$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$- 27 \leq \frac{4 x + 17}{3} \cdot 3 < 7 \cdot 3$

Rewrite the expression.

$- 27 \leq 4 x + 17 < 7 \cdot 3$

Step 4

Multiply $7$ by $3$ .

$- 27 \leq 4 x + 17 < 21$

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.

$- 27 - 17 \leq 4 x < 21 - 17$

Subtract $17$ from $- 27$ .

$- 44 \leq 4 x < 21 - 17$

Subtract $17$ from $21$ .

$- 44 \leq 4 x < 4$

Step 6

Divide each term in the inequality by $4$ .

$\frac{- 44}{4} \leq \frac{4 x}{4} < \frac{4}{4}$

Step 7

Divide $- 44$ by $4$ .

$- 11 \leq \frac{4 x}{4} < \frac{4}{4}$

Step 8

Cancel the common factor of $4$ .

Cancel the common factor.

$- 11 \leq \frac{4 x}{4} < \frac{4}{4}$

Divide $x$ by $1$ .

$- 11 \leq x < \frac{4}{4}$

Step 9

Divide $4$ by $4$ .

$- 11 \leq x < 1$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$- 11 \leq x < 1$

Interval Notation:

$[- 11, 1)$

Step 11

Solve for x -9<=(4x+17)/3<7

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