Algebra Examples

$13 > \frac{2}{3} a - 1$

Step 1

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

$\frac{2}{3} a - 1 < 13$

Step 2

Combine $\frac{2}{3}$ and $a$ .

$\frac{2 a}{3} - 1 < 13$

Step 3

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

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Step 3.1

Add $1$ to both sides of the inequality.

$\frac{2 a}{3} < 13 + 1$

Step 3.2

Add $13$ and $1$ .

$\frac{2 a}{3} < 14$

Step 4

Multiply both sides by $3$ .

$\frac{2 a}{3} \cdot 3 < 14 \cdot 3$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{2 a}{3} \cdot 3 < 14 \cdot 3$

Step 5.1.1.2

Rewrite the expression.

$2 a < 14 \cdot 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $14$ by $3$ .

$2 a < 42$

Step 6

Divide each term in $2 a < 42$ by $2$ and simplify.

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Step 6.1

Divide each term in $2 a < 42$ by $2$ .

$\frac{2 a}{2} < \frac{42}{2}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $2$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{2 a}{2} < \frac{42}{2}$

Step 6.2.1.2

Divide $a$ by $1$ .

$a < \frac{42}{2}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $42$ by $2$ .

$a < 21$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$a < 21$

Interval Notation:

$(- \infty, 21)$