Solve the System of Inequalities 5-m<4 or 7m>35

$5 - m < 4$ or $7 m > 35$

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

$- m < 4 - 5$ or $7 m > 35$

Subtract $5$ from $4$ .

$- m < - 1$ or $7 m > 35$

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

Divide each term in $- m < - 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- m}{- 1} > \frac{- 1}{- 1}$ or $7 m > 35$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{m}{1} > \frac{- 1}{- 1}$ or $7 m > 35$

Divide $m$ by $1$ .

$m > \frac{- 1}{- 1}$ or $7 m > 35$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$m > 1$ or $7 m > 35$

Step 2

Divide each term in $7 m > 35$ by $7$ and simplify.

Divide each term in $7 m > 35$ by $7$ .

$m > 1$ or $\frac{7 m}{7} > \frac{35}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$m > 1$ or $\frac{7 m}{7} > \frac{35}{7}$

Divide $m$ by $1$ .

$m > 1$ or $m > \frac{35}{7}$

Simplify the right side.

Divide $35$ by $7$ .

$m > 1$ or $m > 5$

Step 3

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

$m > 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m > 1$

Interval Notation:

$(1, \infty)$

Step 5

Solve the System of Inequalities 5-m<4 or 7m>35

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