Algebra Examples

$- 4 x > - 9 + 8 (- \frac{3}{2} x + 1) - x$

Step 1

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

$- 9 + 8 (- \frac{3}{2} x + 1) - x < - 4 x$

Step 2

Simplify $- 9 + 8 (- \frac{3}{2} x + 1) - x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Combine $x$ and $\frac{3}{2}$ .

$- 9 + 8 (- \frac{x \cdot 3}{2} + 1) - x < - 4 x$

Step 2.1.1.2

Move $3$ to the left of $x$ .

$- 9 + 8 (- \frac{3 x}{2} + 1) - x < - 4 x$

Step 2.1.2

Apply the distributive property.

$- 9 + 8 (- \frac{3 x}{2}) + 8 \cdot 1 - x < - 4 x$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

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

$- 9 + 8 \frac{- 3 x}{2} + 8 \cdot 1 - x < - 4 x$

Step 2.1.3.2

Factor $2$ out of $8$ .

$- 9 + 2 (4) \frac{- 3 x}{2} + 8 \cdot 1 - x < - 4 x$

Step 2.1.3.3

Cancel the common factor.

$- 9 + 2 \cdot 4 \frac{- 3 x}{2} + 8 \cdot 1 - x < - 4 x$

Step 2.1.3.4

Rewrite the expression.

$- 9 + 4 (- 3 x) + 8 \cdot 1 - x < - 4 x$

Step 2.1.4

Multiply $- 3$ by $4$ .

$- 9 - 12 x + 8 \cdot 1 - x < - 4 x$

Step 2.1.5

Multiply $8$ by $1$ .

$- 9 - 12 x + 8 - x < - 4 x$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- 9$ and $8$ .

$- 12 x - 1 - x < - 4 x$

Step 2.2.2

Subtract $x$ from $- 12 x$ .

$- 13 x - 1 < - 4 x$

Step 3

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

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Step 3.1

Add $4 x$ to both sides of the inequality.

$- 13 x - 1 + 4 x < 0$

Step 3.2

Add $- 13 x$ and $4 x$ .

$- 9 x - 1 < 0$

Step 4

Add $1$ to both sides of the inequality.

$- 9 x < 1$

Step 5

Divide each term in $- 9 x < 1$ by $- 9$ and simplify.

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Step 5.1

Divide each term in $- 9 x < 1$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} > \frac{1}{- 9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} > \frac{1}{- 9}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{- 9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$x > - \frac{1}{9}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{9}$

Interval Notation:

$(- \frac{1}{9}, \infty)$