Question

Simplify the expressions.

$-\frac{3}{4}(5p-12)+2(8-\frac{1}{4}p)$

Answer 1

Simplifying the algebraic expression :

The given algebraic expression is $-\frac{3}{4}(5p-12)+2(8-\frac{1}{4}p)$

$\begin{array}{rcl}-\frac{3}{4}(5\mathrm{p}-12)+2\left(8-\frac{1}{4}\mathrm{p}\right)& =& -\frac{3}{4}(-12)+2\left(8\right)+2\left(-\frac{1}{4}\mathrm{p}\right)\{\mathrm{Distributive}\mathrm{property}\}\\ & =& -\frac{15}{4}\mathrm{p}-(-9)+16+\left(-\frac{1}{2}\mathrm{p}\right)\\ & =& \left[-\frac{15}{4}\mathrm{p}+\left(-\frac{1}{2}\mathrm{p}\right)\right]+\left[9+16\right]\{\mathrm{Commutative}\mathrm{propert}\}\\ & =& \left[-\frac{17}{4}\mathrm{p}\right]+\left[25\right]\{\mathrm{Combine}\mathrm{like}\mathrm{terms}\}\end{array}$

Hence, the simplified expression for given algebraic expression is $\left[-\frac{17}{4}p\right]+\left[25\right]$