Pre-Algebra Examples

$9 (x - 2) > - 16$

Step 1

Divide each term in $9 (x - 2) > - 16$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 (x - 2) > - 16$ by $9$ .

$\frac{9 (x - 2)}{9} > \frac{- 16}{9}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $9$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{9 (x - 2)}{9} > \frac{- 16}{9}$

Step 1.2.1.2

Divide $x - 2$ by $1$ .

$x - 2 > \frac{- 16}{9}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$x - 2 > - \frac{16}{9}$

Step 2

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

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Step 2.1

Add $2$ to both sides of the inequality.

$x > - \frac{16}{9} + 2$

Step 2.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$x > - \frac{16}{9} + 2 \cdot \frac{9}{9}$

Step 2.3

Combine $2$ and $\frac{9}{9}$ .

$x > - \frac{16}{9} + \frac{2 \cdot 9}{9}$

Step 2.4

Combine the numerators over the common denominator.

$x > \frac{- 16 + 2 \cdot 9}{9}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $9$ .

$x > \frac{- 16 + 18}{9}$

Step 2.5.2

Add $- 16$ and $18$ .

$x > \frac{2}{9}$

Step 3