1.1 Real numbers: algebra essentials  (Page 8/35)

1. Substitute 0 for $x.$
   $$\begin{array}{ccc}\hfill 2x-7& =& 2(0)-7\\ & =& 0-7\hfill \\ & =& \mathrm{-7}\hfill \end{array}$$
2. Substitute 1 for $x.$
   $$\begin{array}{ccc}2x-7& =& 2(1)-7\hfill \\ & =& 2-7\hfill \\ & =& \mathrm{-5}\hfill \end{array}$$
3. Substitute $\frac{1}{2}$ for $x.$
   $$\begin{array}{ccc}\hfill 2x-7& =& 2\left(\frac{1}{2}\right)-7\hfill \\ & =& 1-7\hfill \\ & =& \mathrm{-6}\hfill \end{array}$$
4. Substitute $\mathrm{-4}$ for $x.$
   $\begin{array}{ccc}\hfill 2x-7& =& 2(-4)-7\\ & =& -8-7\hfill \\ & =& \mathrm{-15}\hfill \end{array}$

1. Substitute $\mathrm{-5}$ for $x.$
   $$\begin{array}{ccc}\hfill x+5& =& (\mathrm{-5})+5\hfill \\ & =& 0\hfill \end{array}$$
2. Substitute 10 for $t.$
   $$\begin{array}{ccc}\hfill \frac{t}{2t-1}& =& \frac{(10)}{2(10)-1}\hfill \\ & =& \frac{10}{20-1}\hfill \\ & =& \frac{10}{19}\hfill \end{array}$$
3. Substitute 5 for $r.$
   $\begin{array}{ccc}\hfill \frac{4}{3}\pi r^3& =& \frac{4}{3}\pi {(5)}^3\\ & =& \frac{4}{3}\pi (125)\hfill \\ & =& \frac{500}{3}\pi \hfill \end{array}$
4. Substitute 11 for $a$ and –8 for $b.$
   $$\begin{array}{ccc}\hfill a+ab+b& =& (11)+(11)(\mathrm{-8})+(\mathrm{-8})\\ & =& 11-88-8\hfill \\ & =& \mathrm{-85}\hfill \end{array}$$
5. Substitute 2 for $m$ and 3 for $n.$
   $$\begin{array}{ccc}\hfill \sqrt{2m^3{n}^2}& =& \sqrt{2{(2)}^3{(3)}^2}\hfill \\ & =& \sqrt{2(8)(9)}\hfill \\ & =& \sqrt{144}\hfill \\ & =& 12\hfill \end{array}$$

Evaluate the expression $2\pi r\left(r+h\right)$ for $r=6$ and $h=9.$

The surface area is $180\pi$ square inches.

1. 
   $\begin{array}{cccc}\hfill 3x-2y+x-3y-7& =& 3x+x-2y-3y-7\hfill & \text{Commutative property of addition}\hfill \\ & =& 4x-5y-7\hfill & \text{Simplify}\hfill \end{array}$
2. 
   $\begin{array}{cccc}\hfill 2r-5(3-r)+4& =& 2r-15+5r+4\hfill & \text{Distributive property}\hfill \\ & =& 2r+5r-15+4\hfill & \text{Commutative property of addition}\hfill \\ & =& 7r-11\hfill & \text{Simplify}\hfill \end{array}$
3. 
   $\begin{array}{cccc}\hfill 4t-4\left(t-\frac{5}{4}s\right)-\left(\frac{2}{3}t+2s\right)& =& 4t-\frac{5}{4}s-\frac{2}{3}t-2s\hfill & \text{Distributive property}\hfill \\ & =& 4t-\frac{2}{3}t-\frac{5}{4}s-2s\hfill & \text{Commutative property of addition}\hfill \\ & =& \frac{10}{3}t-\frac{13}{4}s\hfill & \text{Simplify}\hfill \end{array}$
4. 
   $\begin{array}{cccc}mn-5m+3mn+n& =& 2mn+3mn-5m+n& \text{Commutative property of addition}\hfill \\ & =& 5mn-5m+n\hfill & \text{Simplify}\hfill \end{array}$