Algebra Examples

$6 m - 2 (7 + 3 m) > 5 (2 m - 3) - m$

Step 1

Simplify $6 m - 2 (7 + 3 m)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$6 m - 2 \cdot 7 - 2 (3 m) > 5 (2 m - 3) - m$

Step 1.1.2

Multiply $- 2$ by $7$ .

$6 m - 14 - 2 (3 m) > 5 (2 m - 3) - m$

Step 1.1.3

Multiply $3$ by $- 2$ .

$6 m - 14 - 6 m > 5 (2 m - 3) - m$

Step 1.2

Combine the opposite terms in $6 m - 14 - 6 m$ .

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Step 1.2.1

Subtract $6 m$ from $6 m$ .

$0 - 14 > 5 (2 m - 3) - m$

Step 1.2.2

Subtract $14$ from $0$ .

$- 14 > 5 (2 m - 3) - m$

Step 2

Simplify $5 (2 m - 3) - m$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 14 > 5 (2 m) + 5 \cdot - 3 - m$

Step 2.1.2

Multiply $2$ by $5$ .

$- 14 > 10 m + 5 \cdot - 3 - m$

Step 2.1.3

Multiply $5$ by $- 3$ .

$- 14 > 10 m - 15 - m$

Step 2.2

Subtract $m$ from $10 m$ .

$- 14 > 9 m - 15$

Step 3

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

$9 m - 15 < - 14$

Step 4

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

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Step 4.1

Add $15$ to both sides of the inequality.

$9 m < - 14 + 15$

Step 4.2

Add $- 14$ and $15$ .

$9 m < 1$

Step 5

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

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Step 5.1

Divide each term in $9 m < 1$ by $9$ .

$\frac{9 m}{9} < \frac{1}{9}$

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.

$\frac{9 m}{9} < \frac{1}{9}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m < \frac{1}{9}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$m < \frac{1}{9}$

Interval Notation:

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