Solve the System of Inequalities 3>=(7-x)/2>=1

$3 \geq \frac{7 - x}{2} \geq 1$

Solve $3 \geq \frac{7 - x}{2}$ for $x$ .

Multiply both sides by $2$ .

$3 \cdot 2 \geq \frac{7 - x}{2} \cdot 2$

Simplify.

Simplify the left side.

Multiply $3$ by $2$ .

$6 \geq \frac{7 - x}{2} \cdot 2$

Simplify the right side.

Simplify $\frac{7 - x}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$6 \geq \frac{7 - x}{2} \cdot 2$

Rewrite the expression.

$6 \geq 7 - x$

Reorder $7$ and $- x$ .

$6 \geq - x + 7$

Solve for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$- x + 7 \leq 6$

Move all terms not containing $x$ to the right side of the inequality.

Subtract $7$ from both sides of the inequality.

$- x \leq 6 - 7$

Subtract $7$ from $6$ .

$- x \leq - 1$

Divide each term in $- x \leq - 1$ by $- 1$ and simplify.

Divide each term in $- x \leq - 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 1}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{- 1}{- 1}$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x \geq 1$

Solve $\frac{7 - x}{2} \geq 1$ for $x$ .

Multiply both sides by $2$ .

$\frac{7 - x}{2} \cdot 2 \geq 1 \cdot 2$

Simplify.

Simplify the left side.

Simplify $\frac{7 - x}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 - x}{2} \cdot 2 \geq 1 \cdot 2$

Rewrite the expression.

$7 - x \geq 1 \cdot 2$

Reorder $7$ and $- x$ .

$- x + 7 \geq 1 \cdot 2$

Simplify the right side.

Multiply $2$ by $1$ .

$- x + 7 \geq 2$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Subtract $7$ from both sides of the inequality.

$- x \geq 2 - 7$

Subtract $7$ from $2$ .

$- x \geq - 5$

Divide each term in $- x \geq - 5$ by $- 1$ and simplify.

Divide each term in $- x \geq - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x \leq 5$

Find the intersection of $x \geq 1$ and $x \leq 5$ .

$1 \leq x \leq 5$

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 5$

Interval Notation:

$[1, 5]$

Solve the System of Inequalities 3>=(7-x)/2>=1

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