Algebra Examples

$5 (x - 3) + 6 x > - 14$

Step 1

Simplify $5 (x - 3) + 6 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$5 x + 5 \cdot - 3 + 6 x > - 14$

Step 1.1.2

Multiply $5$ by $- 3$ .

$5 x - 15 + 6 x > - 14$

Step 1.2

Add $5 x$ and $6 x$ .

$11 x - 15 > - 14$

Step 2

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

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Step 2.1

Add $15$ to both sides of the inequality.

$11 x > - 14 + 15$

Step 2.2

Add $- 14$ and $15$ .

$11 x > 1$

Step 3

Divide each term in $11 x > 1$ by $11$ and simplify.

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Step 3.1

Divide each term in $11 x > 1$ by $11$ .

$\frac{11 x}{11} > \frac{1}{11}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{11 x}{11} > \frac{1}{11}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{11}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{11}$

Interval Notation:

$(\frac{1}{11}, \infty)$