Solve the System of Inequalities 10m-7<17m or -6m>36

$10 m - 7 < 17 m$ or $- 6 m > 36$

Simplify the first inequality.

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

Add $7$ to both sides of the inequality.

$10 m < 17 + 7$ or $- 6 m > 36$

Add $17$ and $7$ .

$10 m < 24$ or $- 6 m > 36$

Divide each term in $10 m < 24$ by $10$ and simplify.

Divide each term in $10 m < 24$ by $10$ .

$\frac{10 m}{10} < \frac{24}{10}$ or $- 6 m > 36$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 m}{10} < \frac{24}{10}$ or $- 6 m > 36$

Divide $m$ by $1$ .

$m < \frac{24}{10}$ or $- 6 m > 36$

Simplify the right side.

Cancel the common factor of $24$ and $10$ .

Factor $2$ out of $24$ .

$m < \frac{2 (12)}{10}$ or $- 6 m > 36$

Cancel the common factors.

Factor $2$ out of $10$ .

$m < \frac{2 \cdot 12}{2 \cdot 5}$ or $- 6 m > 36$

Cancel the common factor.

$m < \frac{2 \cdot 12}{2 \cdot 5}$ or $- 6 m > 36$

Rewrite the expression.

$m < \frac{12}{5}$ or $- 6 m > 36$

Divide each term in $- 6 m > 36$ by $- 6$ and simplify.

Divide each term in $- 6 m > 36$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$m < \frac{12}{5}$ or $\frac{- 6 m}{- 6} < \frac{36}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$m < \frac{12}{5}$ or $\frac{- 6 m}{- 6} < \frac{36}{- 6}$

Divide $m$ by $1$ .

$m < \frac{12}{5}$ or $m < \frac{36}{- 6}$

Simplify the right side.

Divide $36$ by $- 6$ .

$m < \frac{12}{5}$ or $m < - 6$

The union consists of all of the elements that are contained in each interval.

$m < \frac{12}{5}$

The result can be shown in multiple forms.

Inequality Form:

$m < \frac{12}{5}$

Interval Notation:

$(- \infty, \frac{12}{5})$

Solve the System of Inequalities 10m-7<17m or -6m>36

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