Solve the System of Inequalities (m-8)/2<2 OR (3m+1)/2>-1

$\frac{m - 8}{2} < 2$ OR $\frac{3 m + 1}{2} > - 1$

Solve $\frac{m - 8}{2} < 2$ for $m$ .

Multiply both sides by $2$ .

$\frac{m - 8}{2} \cdot 2 < 2 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{m - 8}{2} \cdot 2 < 2 \cdot 2$

Rewrite the expression.

$m - 8 < 2 \cdot 2$

Simplify the right side.

Multiply $2$ by $2$ .

$m - 8 < 4$

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

Add $8$ to both sides of the inequality.

$m < 4 + 8$

Add $4$ and $8$ .

$m < 12$

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

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 m + 1 > - 1 \cdot 2$

Simplify the right side.

Multiply $- 1$ by $2$ .

$3 m + 1 > - 2$

Solve for $m$ .

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

Subtract $1$ from both sides of the inequality.

$3 m > - 2 - 1$

Subtract $1$ from $- 2$ .

$3 m > - 3$

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

Divide each term in $3 m > - 3$ by $3$ .

$\frac{3 m}{3} > \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 m}{3} > \frac{- 3}{3}$

Divide $m$ by $1$ .

$m > \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$m > - 1$

Find the intersection of $m < 12$ and $m > - 1$ .

$- 1 < m < 12$

The result can be shown in multiple forms.

Inequality Form:

$- 1 < m < 12$

Interval Notation:

$(- 1, 12)$

Solve the System of Inequalities (m-8)/2<2 OR (3m+1)/2>-1

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