Solve for x -19<=5-6x<29

$- 19 \leq 5 - 6 x < 29$

Step 1

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.

$- 19 - 5 \leq - 6 x < 29 - 5$

Subtract $5$ from $- 19$ .

$- 24 \leq - 6 x < 29 - 5$

Subtract $5$ from $29$ .

$- 24 \leq - 6 x < 24$

Step 2

Divide each term in the inequality by $- 6$ .

$\frac{- 24}{- 6} \geq \frac{- 6 x}{- 6} > \frac{24}{- 6}$

Step 3

Divide $- 24$ by $- 6$ .

$4 \geq \frac{- 6 x}{- 6} > \frac{24}{- 6}$

Step 4

Cancel the common factor of $- 6$ .

Cancel the common factor.

$4 \geq \frac{- 6 x}{- 6} > \frac{24}{- 6}$

Divide $x$ by $1$ .

$4 \geq x > \frac{24}{- 6}$

Step 5

Divide $24$ by $- 6$ .

$4 \geq x > - 4$

Step 6

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

$- 4 < x \leq 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 < x \leq 4$

Interval Notation:

$(- 4, 4]$

Step 8