Solve for m (2m+3)/2-17/4<(m+2)/8

$\frac{2 m + 3}{2} - \frac{17}{4} < \frac{m + 2}{8}$

Multiply both sides by $8$ .

$(\frac{2 m + 3}{2} - \frac{17}{4}) \cdot 8 < \frac{m + 2}{8} \cdot 8$

Simplify.

Simplify the left side.

Simplify $(\frac{2 m + 3}{2} - \frac{17}{4}) \cdot 8$ .

To write $\frac{2 m + 3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{2 m + 3}{2} \cdot \frac{2}{2} - \frac{17}{4}) \cdot 8 < \frac{m + 2}{8} \cdot 8$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 m + 3}{2}$ by $\frac{2}{2}$ .

$(\frac{(2 m + 3) \cdot 2}{2 \cdot 2} - \frac{17}{4}) \cdot 8 < \frac{m + 2}{8} \cdot 8$

Multiply $2$ by $2$ .

$(\frac{(2 m + 3) \cdot 2}{4} - \frac{17}{4}) \cdot 8 < \frac{m + 2}{8} \cdot 8$

Combine the numerators over the common denominator.

$\frac{(2 m + 3) \cdot 2 - 17}{4} \cdot 8 < \frac{m + 2}{8} \cdot 8$

Simplify the numerator.

Apply the distributive property.

$\frac{2 m \cdot 2 + 3 \cdot 2 - 17}{4} \cdot 8 < \frac{m + 2}{8} \cdot 8$

Multiply $2$ by $2$ .

$\frac{4 m + 3 \cdot 2 - 17}{4} \cdot 8 < \frac{m + 2}{8} \cdot 8$

Multiply $3$ by $2$ .

$\frac{4 m + 6 - 17}{4} \cdot 8 < \frac{m + 2}{8} \cdot 8$

Subtract $17$ from $6$ .

$\frac{4 m - 11}{4} \cdot 8 < \frac{m + 2}{8} \cdot 8$

Simplify terms.

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{4 m - 11}{4} \cdot (4 (2)) < \frac{m + 2}{8} \cdot 8$

Cancel the common factor.

$\frac{4 m - 11}{4} \cdot (4 \cdot 2) < \frac{m + 2}{8} \cdot 8$

Rewrite the expression.

$(4 m - 11) \cdot 2 < \frac{m + 2}{8} \cdot 8$

Apply the distributive property.

$4 m \cdot 2 - 11 \cdot 2 < \frac{m + 2}{8} \cdot 8$

Multiply.

Multiply $2$ by $4$ .

$8 m - 11 \cdot 2 < \frac{m + 2}{8} \cdot 8$

Multiply $- 11$ by $2$ .

$8 m - 22 < \frac{m + 2}{8} \cdot 8$

Simplify the right side.

Cancel the common factor of $8$ .

Cancel the common factor.

$8 m - 22 < \frac{m + 2}{8} \cdot 8$

Rewrite the expression.

$8 m - 22 < m + 2$

Solve for $m$ .

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

Subtract $m$ from both sides of the inequality.

$8 m - 22 - m < 2$

Subtract $m$ from $8 m$ .

$7 m - 22 < 2$

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

Add $22$ to both sides of the inequality.

$7 m < 2 + 22$

Add $2$ and $22$ .

$7 m < 24$

Divide each term in $7 m < 24$ by $7$ and simplify.

Divide each term in $7 m < 24$ by $7$ .

$\frac{7 m}{7} < \frac{24}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 m}{7} < \frac{24}{7}$

Divide $m$ by $1$ .

$m < \frac{24}{7}$

The result can be shown in multiple forms.

Inequality Form:

$m < \frac{24}{7}$

Interval Notation:

$(- \infty, \frac{24}{7})$

Solve for m (2m+3)/2-17/4<(m+2)/8

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