Solve the Inequality for x 1<=1/2x+1<=3

$1 \leq \frac{1}{2} x + 1 \leq 3$

Step 1

Combine $\frac{1}{2}$ and $x$ .

$1 \leq \frac{x}{2} + 1 \leq 3$

Step 2

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$1 - 1 \leq \frac{x}{2} \leq 3 - 1$

Subtract $1$ from $1$ .

$0 \leq \frac{x}{2} \leq 3 - 1$

Multiply each term in the inequality by $2$ .

$0 \cdot 2 \leq \frac{x}{2} \cdot 2 \leq 3 \cdot 2 - 1 \cdot 2$

Multiply $0$ by $2$ .

$0 \leq \frac{x}{2} \cdot 2 \leq 3 \cdot 2 - 1 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$0 \leq \frac{x}{2} \cdot 2 \leq 3 \cdot 2 - 1 \cdot 2$

Rewrite the expression.

$0 \leq x \leq 3 \cdot 2 - 1 \cdot 2$

Simplify each term.

Multiply $3$ by $2$ .

$0 \leq x \leq 6 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$0 \leq x \leq 6 - 2$

Subtract $2$ from $6$ .

$0 \leq x \leq 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$0 \leq x \leq 4$

Interval Notation:

$[0, 4]$

Step 4