Algebra Examples

$\frac{1 + m}{9} \geq 1$

Step 1

Multiply both sides by $9$ .

$\frac{1 + m}{9} \cdot 9 \geq 1 \cdot 9$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{1 + m}{9} \cdot 9$ .

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Step 2.1.1.1

Cancel the common factor of $9$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{1 + m}{9} \cdot 9 \geq 1 \cdot 9$

Step 2.1.1.1.2

Rewrite the expression.

$1 + m \geq 1 \cdot 9$

$1 + m \geq 1 \cdot 9$

Step 2.1.1.2

Reorder $1$ and $m$ .

$m + 1 \geq 1 \cdot 9$

$m + 1 \geq 1 \cdot 9$

$m + 1 \geq 1 \cdot 9$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $9$ by $1$ .

$m + 1 \geq 9$

$m + 1 \geq 9$

$m + 1 \geq 9$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the inequality.

$m \geq 9 - 1$

Step 3.2

Subtract $1$ from $9$ .

$m \geq 8$

$m \geq 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m \geq 8$

Interval Notation:

$[8, \infty)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$