Algebra Examples

$\frac{a - 2}{3} > a + 4$

Step 1

Multiply both sides by $3$ .

$\frac{a - 2}{3} \cdot 3 > (a + 4) \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{a - 2}{3} \cdot 3 > (a + 4) \cdot 3$

Step 2.1.1.2

Rewrite the expression.

$a - 2 > (a + 4) \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(a + 4) \cdot 3$ .

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Step 2.2.1.1

Apply the distributive property.

$a - 2 > a \cdot 3 + 4 \cdot 3$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $3$ to the left of $a$ .

$a - 2 > 3 \cdot a + 4 \cdot 3$

Step 2.2.1.2.2

Multiply $4$ by $3$ .

$a - 2 > 3 a + 12$

Step 3

Solve for $a$ .

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Step 3.1

Move all terms containing $a$ to the left side of the inequality.

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Step 3.1.1

Subtract $3 a$ from both sides of the inequality.

$a - 2 - 3 a > 12$

Step 3.1.2

Subtract $3 a$ from $a$ .

$- 2 a - 2 > 12$

Step 3.2

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

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Step 3.2.1

Add $2$ to both sides of the inequality.

$- 2 a > 12 + 2$

Step 3.2.2

Add $12$ and $2$ .

$- 2 a > 14$

Step 3.3

Divide each term in $- 2 a > 14$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 a > 14$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

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

Step 3.3.2.1.2

Divide $a$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $14$ by $- 2$ .

$a < - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a < - 7$

Interval Notation:

$(- \infty, - 7)$