Finite Math Examples

$m < 3 - m < 1$

Step 1

Move all terms not containing $m$ from the center section of the inequality.

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Step 1.1

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$m - 3 < - m < 1 - 3$

Step 1.2

Subtract $3$ from $1$ .

$m - 3 < - m < - 2$

Step 2

Multiply each term in the inequality by $- 1$ .

$\frac{m}{- 1} + \frac{- 3}{- 1} > \frac{- m}{- 1} > \frac{- 2}{- 1}$

Step 3

Simplify each term.

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Step 3.1

Move the negative one from the denominator of $\frac{m}{- 1}$ .

$- 1 \cdot m + \frac{- 3}{- 1} > \frac{- m}{- 1} > \frac{- 2}{- 1}$

Step 3.2

Rewrite $- 1 \cdot m$ as $- m$ .

$- m + \frac{- 3}{- 1} > \frac{- m}{- 1} > \frac{- 2}{- 1}$

Step 3.3

Divide $- 3$ by $- 1$ .

$- m + 3 > \frac{- m}{- 1} > \frac{- 2}{- 1}$

Step 4

Dividing two negative values results in a positive value.

$- m + 3 > \frac{m}{1} > \frac{- 2}{- 1}$

Step 5

Divide $m$ by $1$ .

$- m + 3 > m > \frac{- 2}{- 1}$

Step 6

Divide $- 2$ by $- 1$ .

$- m + 3 > m > 2$

Step 7

Convert the inequality to interval notation.

$(- m + 3, 2)$

Step 8