Algebra Examples

$- 4 < 2 x + 1 < 7$

Step 1

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

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Step 1.1

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

$- 4 - 1 < 2 x < 7 - 1$

Step 1.2

Subtract $1$ from $- 4$ .

$- 5 < 2 x < 7 - 1$

Step 1.3

Subtract $1$ from $7$ .

$- 5 < 2 x < 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 5}{2} < \frac{2 x}{2} < \frac{6}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{5}{2} < \frac{2 x}{2} < \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$- \frac{5}{2} < \frac{2 x}{2} < \frac{6}{2}$

Step 4.2

Divide $x$ by $1$ .

$- \frac{5}{2} < x < \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- \frac{5}{2} < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{5}{2} < x < 3$

Interval Notation:

$(- \frac{5}{2}, 3)$

Step 7