# Calculate: -(1)/(4) * (p+7)+(5)/(2) * (2p-5) < 9

## Expression: $-\frac{ 1 }{ 4 } \times \left( p+7 \right)+\frac{ 5 }{ 2 } \times \left( 2p-5 \right) < 9$

Distribute $-\frac{ 1 }{ 4 }$ through the parentheses

$-\frac{ 1 }{ 4 }p-\frac{ 7 }{ 4 }+\frac{ 5 }{ 2 } \times \left( 2p-5 \right) < 9$

Distribute $\frac{ 5 }{ 2 }$ through the parentheses

$-\frac{ 1 }{ 4 }p-\frac{ 7 }{ 4 }+5p-\frac{ 25 }{ 2 } < 9$

Calculate the difference

$-\frac{ 1 }{ 4 }p-\frac{ 57 }{ 4 }+5p < 9$

Multiply both sides of the inequality by $4$

$-p-57+20p < 36$

Collect like terms

$19p-57 < 36$

Move the constant to the right-hand side and change its sign

$19p < 36+57$

$19p < 93$
Divide both sides of the inequality by $19$
\begin{align*}&p < \frac{ 93 }{ 19 } \\&\begin{array} { l }\begin{array} { l }\begin{array} { l }p < 4 \frac{ 17 }{ 19 },& p < 4.\overset{ \cdot }{ 8 } 9473684210526315\overset{ \cdot }{ 7 } \end{array},& p \in \langle-\infty, \frac{ 93 }{ 19 }\rangle\end{array}\end{array}\end{align*}