Solve the System of Inequalities 6+7m<6m-5 or 3m-7<5+6m

$6 + 7 m < 6 m - 5$ or $3 m - 7 < 5 + 6 m$

Step 1

Simplify the first inequality.

Move all terms containing $m$ to the left side of the inequality.

Subtract $6 m$ from both sides of the inequality.

$6 + 7 m - 6 m < - 5$ or $3 m - 7 < 5 + 6 m$

Subtract $6 m$ from $7 m$ .

$6 + m < - 5$ or $3 m - 7 < 5 + 6 m$

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

Subtract $6$ from both sides of the inequality.

$m < - 5 - 6$ or $3 m - 7 < 5 + 6 m$

Subtract $6$ from $- 5$ .

$m < - 11$ or $3 m - 7 < 5 + 6 m$

Step 2

Simplify the second inequality.

Move all terms containing $m$ to the left side of the inequality.

Subtract $6 m$ from both sides of the inequality.

$m < - 11$ or $3 m - 7 - 6 m < 5$

Subtract $6 m$ from $3 m$ .

$m < - 11$ or $- 3 m - 7 < 5$

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

Add $7$ to both sides of the inequality.

$m < - 11$ or $- 3 m < 5 + 7$

Add $5$ and $7$ .

$m < - 11$ or $- 3 m < 12$

Divide each term in $- 3 m < 12$ by $- 3$ and simplify.

Divide each term in $- 3 m < 12$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$m < - 11$ or $\frac{- 3 m}{- 3} > \frac{12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$m < - 11$ or $\frac{- 3 m}{- 3} > \frac{12}{- 3}$

Divide $m$ by $1$ .

$m < - 11$ or $m > \frac{12}{- 3}$

Simplify the right side.

Divide $12$ by $- 3$ .

$m < - 11$ or $m > - 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$m < - 11 or m > - 4$

Interval Notation:

$(- \infty, - 11) \cup (- 4, \infty)$

Step 4

Solve the System of Inequalities 6+7m<6m-5 or 3m-7<5+6m

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