Pre-Algebra Examples

$9 x + 22 > 7$

Step 1

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

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Step 1.1

Subtract $22$ from both sides of the inequality.

$9 x > 7 - 22$

Step 1.2

Subtract $22$ from $7$ .

$9 x > - 15$

Step 2

Divide each term in $9 x > - 15$ by $9$ and simplify.

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Step 2.1

Divide each term in $9 x > - 15$ by $9$ .

$\frac{9 x}{9} > \frac{- 15}{9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} > \frac{- 15}{9}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 15}{9}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $- 15$ and $9$ .

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Step 2.3.1.1

Factor $3$ out of $- 15$ .

$x > \frac{3 (- 5)}{9}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $3$ out of $9$ .

$x > \frac{3 \cdot - 5}{3 \cdot 3}$

Step 2.3.1.2.2

Cancel the common factor.

$x > \frac{3 \cdot - 5}{3 \cdot 3}$

Step 2.3.1.2.3

Rewrite the expression.

$x > \frac{- 5}{3}$

Step 2.3.2

Move the negative in front of the fraction.

$x > - \frac{5}{3}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{5}{3}$

Interval Notation:

$(- \frac{5}{3}, \infty)$