Pre-Algebra Examples

$3 x + 2 < 4 x - 5 < 2 x + 11$

Step 1

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

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Step 1.1

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$3 x + 2 + 5 < 4 x < 2 x + 11 + 5$

Step 1.2

Add $2$ and $5$ .

$3 x + 7 < 4 x < 2 x + 11 + 5$

Step 1.3

Add $11$ and $5$ .

$3 x + 7 < 4 x < 2 x + 16$

Step 2

Divide each term in the inequality by $4$ .

$\frac{3 x}{4} + \frac{7}{4} < \frac{4 x}{4} < \frac{2 x}{4} + \frac{16}{4}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$\frac{3 x}{4} + \frac{7}{4} < \frac{4 x}{4} < \frac{2 x}{4} + \frac{16}{4}$

Step 3.2

Divide $x$ by $1$ .

$\frac{3 x}{4} + \frac{7}{4} < x < \frac{2 x}{4} + \frac{16}{4}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ and $4$ .

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Step 4.1.1

Factor $2$ out of $2 x$ .

$\frac{3 x}{4} + \frac{7}{4} < x < \frac{2 (x)}{4} + \frac{16}{4}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $4$ .

$\frac{3 x}{4} + \frac{7}{4} < x < \frac{2 x}{2 \cdot 2} + \frac{16}{4}$

Step 4.1.2.2

Cancel the common factor.

$\frac{3 x}{4} + \frac{7}{4} < x < \frac{2 x}{2 \cdot 2} + \frac{16}{4}$

Step 4.1.2.3

Rewrite the expression.

$\frac{3 x}{4} + \frac{7}{4} < x < \frac{x}{2} + \frac{16}{4}$

Step 4.2

Divide $16$ by $4$ .

$\frac{3 x}{4} + \frac{7}{4} < x < \frac{x}{2} + 4$

Step 5