Solve for x -3<=(x-4)/-4<4

$- 3 \leq \frac{x - 4}{- 4} < 4$

Step 1

Move the negative in front of the fraction.

$- 3 \leq - \frac{x - 4}{4} < 4$

Step 2

Multiply each term in the inequality by $4$ .

$- 3 \cdot 4 \leq - \frac{x - 4}{4} \cdot 4 < 4 \cdot 4$

Step 3

Multiply $- 3$ by $4$ .

$- 12 \leq - \frac{x - 4}{4} \cdot 4 < 4 \cdot 4$

Step 4

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x - 4}{4}$ into the numerator.

$- 12 \leq \frac{- (x - 4)}{4} \cdot 4 < 4 \cdot 4$

Cancel the common factor.

$- 12 \leq \frac{- (x - 4)}{4} \cdot 4 < 4 \cdot 4$

Rewrite the expression.

$- 12 \leq - (x - 4) < 4 \cdot 4$

Step 5

Apply the distributive property.

$- 12 \leq - x + 4 < 4 \cdot 4$

Step 6

Multiply $4$ by $4$ .

$- 12 \leq - x + 4 < 16$

Step 7

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

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 - 4 \leq - x < 16 - 4$

Subtract $4$ from $- 12$ .

$- 16 \leq - x < 16 - 4$

Subtract $4$ from $16$ .

$- 16 \leq - x < 12$

Step 8

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

$\frac{- 16}{- 1} \geq \frac{- x}{- 1} > \frac{12}{- 1}$

Step 9

Divide $- 16$ by $- 1$ .

$16 \geq \frac{- x}{- 1} > \frac{12}{- 1}$

Step 10

Dividing two negative values results in a positive value.

$16 \geq \frac{x}{1} > \frac{12}{- 1}$

Step 11

Divide $x$ by $1$ .

$16 \geq x > \frac{12}{- 1}$

Step 12

Divide $12$ by $- 1$ .

$16 \geq x > - 12$

Step 13

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

$- 12 < x \leq 16$

Step 14

The result can be shown in multiple forms.

Inequality Form:

$- 12 < x \leq 16$

Interval Notation:

$(- 12, 16]$

Step 15

Solve for x -3<=(x-4)/-4<4

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