Solve the System of @WORD -3<=5-2x<3

$- 3 \leq 5 - 2 x < 3$

Step 1

Solve $- 3 \leq 5 - 2 x$ for $x$ .

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

$5 - 2 x \geq - 3$

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

Subtract $5$ from both sides of the inequality.

$- 2 x \geq - 3 - 5$

Subtract $5$ from $- 3$ .

$- 2 x \geq - 8$

Divide each term in $- 2 x \geq - 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq - 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{- 8}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$x \leq 4$

Step 2

Solve $5 - 2 x < 3$ for $x$ .

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

Subtract $5$ from both sides of the inequality.

$- 2 x < 3 - 5$

Subtract $5$ from $3$ .

$- 2 x < - 2$

Divide each term in $- 2 x < - 2$ by $- 2$ and simplify.

Divide each term in $- 2 x < - 2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{- 2}{- 2}$

Divide $x$ by $1$ .

$x > \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$x > 1$

Step 3

Find the intersection of $x \leq 4$ and $x > 1$ .

$1 < x \leq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 < x \leq 4$

Interval Notation:

$(1, 4]$

Step 5

Solve the System of @WORD -3<=5-2x<3

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