Solve the System of @WORD -5<=2x+1<7

$- 5 \leq 2 x + 1 < 7$

Step 1

Solve $- 5 \leq 2 x + 1$ for $x$ .

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

$2 x + 1 \geq - 5$

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

Subtract $1$ from both sides of the inequality.

$2 x \geq - 5 - 1$

Subtract $1$ from $- 5$ .

$2 x \geq - 6$

Divide each term in $2 x \geq - 6$ by $2$ and simplify.

Divide each term in $2 x \geq - 6$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $2$ .

$x \geq - 3$

Step 2

Solve $2 x + 1 < 7$ for $x$ .

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

Subtract $1$ from both sides of the inequality.

$2 x < 7 - 1$

Subtract $1$ from $7$ .

$2 x < 6$

Divide each term in $2 x < 6$ by $2$ and simplify.

Divide each term in $2 x < 6$ by $2$ .

$\frac{2 x}{2} < \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{6}{2}$

Divide $x$ by $1$ .

$x < \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x < 3$

Step 3

Find the intersection of $x \geq - 3$ and $x < 3$ .

$- 3 \leq x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < 3$

Interval Notation:

$[- 3, 3)$

Step 5

Solve the System of @WORD -5<=2x+1<7

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