Algebra Examples

$x \div 4 > x - 12$

Step 1

Multiply both sides by $4$ .

$x \div 4 \cdot 4 > (x - 12) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $x \div 4 \cdot 4$ .

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Step 2.1.1.1

Rewrite the division as a fraction.

$\frac{x}{4} \cdot 4 > (x - 12) \cdot 4$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{x}{4} \cdot 4 > (x - 12) \cdot 4$

Step 2.1.1.2.2

Rewrite the expression.

$x > (x - 12) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(x - 12) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

$x > x \cdot 4 - 12 \cdot 4$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Move $4$ to the left of $x$ .

$x > 4 \cdot x - 12 \cdot 4$

Step 2.2.1.2.2

Multiply $- 12$ by $4$ .

$x > 4 x - 48$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4 x$ from both sides of the inequality.

$x - 4 x > - 48$

Step 3.1.2

Subtract $4 x$ from $x$ .

$- 3 x > - 48$

Step 3.2

Divide each term in $- 3 x > - 48$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 x > - 48$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} < \frac{- 48}{- 3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} < \frac{- 48}{- 3}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 48}{- 3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 48$ by $- 3$ .

$x < 16$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 16$

Interval Notation:

$(- \infty, 16)$