Algebra Examples

$- 3 (2 x + 1) > - 2 (x + 4)$

Step 1

Simplify $- 3 (2 x + 1)$ .

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Step 1.1

Rewrite.

$0 + 0 - 3 (2 x + 1) > - 2 (x + 4)$

Step 1.2

Simplify by adding zeros.

$- 3 (2 x + 1) > - 2 (x + 4)$

Step 1.3

Apply the distributive property.

$- 3 (2 x) - 3 \cdot 1 > - 2 (x + 4)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $- 3$ .

$- 6 x - 3 \cdot 1 > - 2 (x + 4)$

Step 1.4.2

Multiply $- 3$ by $1$ .

$- 6 x - 3 > - 2 (x + 4)$

Step 2

Simplify $- 2 (x + 4)$ .

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Step 2.1

Apply the distributive property.

$- 6 x - 3 > - 2 x - 2 \cdot 4$

Step 2.2

Multiply $- 2$ by $4$ .

$- 6 x - 3 > - 2 x - 8$

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.

$- 6 x - 3 + 2 x > - 8$

Step 3.2

Add $- 6 x$ and $2 x$ .

$- 4 x - 3 > - 8$

Step 4

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

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Step 4.1

Add $3$ to both sides of the inequality.

$- 4 x > - 8 + 3$

Step 4.2

Add $- 8$ and $3$ .

$- 4 x > - 5$

Step 5

Divide each term in $- 4 x > - 5$ by $- 4$ and simplify.

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Step 5.1

Divide each term in $- 4 x > - 5$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 5}{- 4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 5}{- 4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 5}{- 4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$x < \frac{5}{4}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{5}{4}$

Interval Notation:

$(- \infty, \frac{5}{4})$