Solve the Inequality for x -5<(x-4)/2<=1

$- 5 < \frac{x - 4}{2} \leq 1$

Step 1

Multiply each term in the inequality by $2$ .

$- 5 \cdot 2 < \frac{x - 4}{2} \cdot 2 \leq 1 \cdot 2$

Step 2

Multiply $- 5$ by $2$ .

$- 10 < \frac{x - 4}{2} \cdot 2 \leq 1 \cdot 2$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$- 10 < \frac{x - 4}{2} \cdot 2 \leq 1 \cdot 2$

Rewrite the expression.

$- 10 < x - 4 \leq 1 \cdot 2$

Step 4

Multiply $2$ by $1$ .

$- 10 < x - 4 \leq 2$

Step 5

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

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

$- 10 + 4 < x \leq 2 + 4$

Add $- 10$ and $4$ .

$- 6 < x \leq 2 + 4$

Add $2$ and $4$ .

$- 6 < x \leq 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x \leq 6$

Interval Notation:

$(- 6, 6]$

Step 7