Algebra Examples

$3 \leq \frac{2 x + 1}{3} \leq 9$

Step 1

Multiply each term in the inequality by $3$ .

$3 \cdot 3 \leq \frac{2 x + 1}{3} \cdot 3 \leq 9 \cdot 3$

Step 2

Multiply $3$ by $3$ .

$9 \leq \frac{2 x + 1}{3} \cdot 3 \leq 9 \cdot 3$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$9 \leq \frac{2 x + 1}{3} \cdot 3 \leq 9 \cdot 3$

Step 3.2

Rewrite the expression.

$9 \leq 2 x + 1 \leq 9 \cdot 3$

Step 4

Multiply $9$ by $3$ .

$9 \leq 2 x + 1 \leq 27$

Step 5

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

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Step 5.1

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

$9 - 1 \leq 2 x \leq 27 - 1$

Step 5.2

Subtract $1$ from $9$ .

$8 \leq 2 x \leq 27 - 1$

Step 5.3

Subtract $1$ from $27$ .

$8 \leq 2 x \leq 26$

Step 6

Divide each term in the inequality by $2$ .

$\frac{8}{2} \leq \frac{2 x}{2} \leq \frac{26}{2}$

Step 7

Divide $8$ by $2$ .

$4 \leq \frac{2 x}{2} \leq \frac{26}{2}$

Step 8

Cancel the common factor of $2$ .

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Step 8.1

Cancel the common factor.

$4 \leq \frac{2 x}{2} \leq \frac{26}{2}$

Step 8.2

Divide $x$ by $1$ .

$4 \leq x \leq \frac{26}{2}$

Step 9

Divide $26$ by $2$ .

$4 \leq x \leq 13$

Step 10

The result can be shown in multiple forms.

Inequality Form:

$4 \leq x \leq 13$

Interval Notation:

$[4, 13]$

Step 11