Algebra Examples

$- \frac{2}{3} (6 x - 12) < \frac{1}{2} (8 - 4 x)$

Step 1

Simplify $- \frac{2}{3} \cdot (6 x - 12)$ .

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Step 1.1

Rewrite.

$0 + 0 - \frac{2}{3} \cdot (6 x - 12) < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.2

Simplify by adding zeros.

$- \frac{2}{3} \cdot (6 x - 12) < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.3

Apply the distributive property.

$- \frac{2}{3} (6 x) - \frac{2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (6 x) - \frac{2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.4.2

Factor $3$ out of $6 x$ .

$\frac{- 2}{3} (3 (2 x)) - \frac{2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.4.3

Cancel the common factor.

$\frac{- 2}{3} (3 (2 x)) - \frac{2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.4.4

Rewrite the expression.

$- 2 (2 x) - \frac{2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.5

Multiply $2$ by $- 2$ .

$- 4 x - \frac{2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$- 4 x + \frac{- 2}{3} \cdot - 12 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.6.2

Factor $3$ out of $- 12$ .

$- 4 x + \frac{- 2}{3} \cdot (3 (- 4)) < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.6.3

Cancel the common factor.

$- 4 x + \frac{- 2}{3} \cdot (3 \cdot - 4) < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.6.4

Rewrite the expression.

$- 4 x - 2 \cdot - 4 < \frac{1}{2} \cdot (8 - 4 x)$

Step 1.7

Multiply $- 2$ by $- 4$ .

$- 4 x + 8 < \frac{1}{2} \cdot (8 - 4 x)$

Step 2

Simplify $\frac{1}{2} \cdot (8 - 4 x)$ .

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Step 2.1

Apply the distributive property.

$- 4 x + 8 < \frac{1}{2} \cdot 8 + \frac{1}{2} (- 4 x)$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $8$ .

$- 4 x + 8 < \frac{1}{2} \cdot (2 (4)) + \frac{1}{2} (- 4 x)$

Step 2.2.2

Cancel the common factor.

$- 4 x + 8 < \frac{1}{2} \cdot (2 \cdot 4) + \frac{1}{2} (- 4 x)$

Step 2.2.3

Rewrite the expression.

$- 4 x + 8 < 4 + \frac{1}{2} (- 4 x)$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $- 4 x$ .

$- 4 x + 8 < 4 + \frac{1}{2} (2 (- 2 x))$

Step 2.3.2

Cancel the common factor.

$- 4 x + 8 < 4 + \frac{1}{2} (2 (- 2 x))$

Step 2.3.3

Rewrite the expression.

$- 4 x + 8 < 4 - 2 x$

Step 3

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

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Step 3.1

Add $2 x$ to both sides of the inequality.

$- 4 x + 8 + 2 x < 4$

Step 3.2

Add $- 4 x$ and $2 x$ .

$- 2 x + 8 < 4$

Step 4

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

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Step 4.1

Subtract $8$ from both sides of the inequality.

$- 2 x < 4 - 8$

Step 4.2

Subtract $8$ from $4$ .

$- 2 x < - 4$

Step 5

Divide each term in $- 2 x < - 4$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 x < - 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{- 4}{- 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{- 4}{- 2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 4}{- 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 4$ by $- 2$ .

$x > 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$