Pre-Algebra Examples

$3 < 4 x + 13 < 21$

Step 1

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

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Step 1.1

Subtract $13$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$3 - 13 < 4 x < 21 - 13$

Step 1.2

Subtract $13$ from $3$ .

$- 10 < 4 x < 21 - 13$

Step 1.3

Subtract $13$ from $21$ .

$- 10 < 4 x < 8$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 10}{4} < \frac{4 x}{4} < \frac{8}{4}$

Step 3

Cancel the common factor of $- 10$ and $4$ .

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Step 3.1

Factor $2$ out of $- 10$ .

$\frac{2 (- 5)}{4} < \frac{4 x}{4} < \frac{8}{4}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot - 5}{2 \cdot 2} < \frac{4 x}{4} < \frac{8}{4}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \cdot - 5}{2 \cdot 2} < \frac{4 x}{4} < \frac{8}{4}$

Step 3.2.3

Rewrite the expression.

$\frac{- 5}{2} < \frac{4 x}{4} < \frac{8}{4}$

Step 4

Move the negative in front of the fraction.

$- \frac{5}{2} < \frac{4 x}{4} < \frac{8}{4}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Cancel the common factor.

$- \frac{5}{2} < \frac{4 x}{4} < \frac{8}{4}$

Step 5.2

Divide $x$ by $1$ .

$- \frac{5}{2} < x < \frac{8}{4}$

Step 6

Divide $8$ by $4$ .

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

Step 7