Algebra Examples

$- 9 x > 9 + 3 (- \frac{1}{3} x + 1) - 3 x$

Step 1

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

$9 + 3 (- \frac{1}{3} x + 1) - 3 x < - 9 x$

Step 2

Simplify $9 + 3 (- \frac{1}{3} x + 1) - 3 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $x$ and $\frac{1}{3}$ .

$9 + 3 (- \frac{x}{3} + 1) - 3 x < - 9 x$

Step 2.1.2

Apply the distributive property.

$9 + 3 (- \frac{x}{3}) + 3 \cdot 1 - 3 x < - 9 x$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

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

$9 + 3 \frac{- x}{3} + 3 \cdot 1 - 3 x < - 9 x$

Step 2.1.3.2

Cancel the common factor.

$9 + 3 \frac{- x}{3} + 3 \cdot 1 - 3 x < - 9 x$

Step 2.1.3.3

Rewrite the expression.

$9 - x + 3 \cdot 1 - 3 x < - 9 x$

Step 2.1.4

Multiply $3$ by $1$ .

$9 - x + 3 - 3 x < - 9 x$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $9$ and $3$ .

$- x + 12 - 3 x < - 9 x$

Step 2.2.2

Subtract $3 x$ from $- x$ .

$- 4 x + 12 < - 9 x$

Step 3

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

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Step 3.1

Add $9 x$ to both sides of the inequality.

$- 4 x + 12 + 9 x < 0$

Step 3.2

Add $- 4 x$ and $9 x$ .

$5 x + 12 < 0$

Step 4

Subtract $12$ from both sides of the inequality.

$5 x < - 12$

Step 5

Divide each term in $5 x < - 12$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 x < - 12$ by $5$ .

$\frac{5 x}{5} < \frac{- 12}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 x}{5} < \frac{- 12}{5}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 12}{5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x < - \frac{12}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{12}{5}$

Interval Notation:

$(- \infty, - \frac{12}{5})$