Pre-Algebra Examples

$- 6 (2 x + 1) < 5 - (x - 4) - 6 x$

Step 1

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

$5 - (x - 4) - 6 x > - 6 (2 x + 1)$

Step 2

Simplify $5 - (x - 4) - 6 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$5 - x - - 4 - 6 x > - 6 (2 x + 1)$

Step 2.1.2

Multiply $- 1$ by $- 4$ .

$5 - x + 4 - 6 x > - 6 (2 x + 1)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $5$ and $4$ .

$- x + 9 - 6 x > - 6 (2 x + 1)$

Step 2.2.2

Subtract $6 x$ from $- x$ .

$- 7 x + 9 > - 6 (2 x + 1)$

Step 3

Simplify $- 6 (2 x + 1)$ .

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Step 3.1

Apply the distributive property.

$- 7 x + 9 > - 6 (2 x) - 6 \cdot 1$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $2$ by $- 6$ .

$- 7 x + 9 > - 12 x - 6 \cdot 1$

Step 3.2.2

Multiply $- 6$ by $1$ .

$- 7 x + 9 > - 12 x - 6$

Step 4

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

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Step 4.1

Add $12 x$ to both sides of the inequality.

$- 7 x + 9 + 12 x > - 6$

Step 4.2

Add $- 7 x$ and $12 x$ .

$5 x + 9 > - 6$

Step 5

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

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Step 5.1

Subtract $9$ from both sides of the inequality.

$5 x > - 6 - 9$

Step 5.2

Subtract $9$ from $- 6$ .

$5 x > - 15$

Step 6

Divide each term in $5 x > - 15$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 x > - 15$ by $5$ .

$\frac{5 x}{5} > \frac{- 15}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} > \frac{- 15}{5}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 15}{5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 15$ by $5$ .

$x > - 3$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > - 3$

Interval Notation:

$(- 3, \infty)$