Question: answer in text simplet answering form
1. Consider the rule $$R = 5b - 3$$.
(a) Find $$R$$ if $$b = 2$$:
$$R = 5(2) - 3 = 10 - 3 = 7$$
(b) Find $$R$$ if $$b = 23$$:
$$R = 5(23) - 3 = 115 - 3 = 112$$
(c) Find $$R$$ if $$b = 7$$:
$$R = 5(7) - 3 = 35 - 3 = 32$$
(d) Find $$R$$ if $$b = 30$$:
$$R = 5(30) - 3 = 150 - 3 = 147$$
2. Consider the rule $$T = 2n + 1$$.
(a) Find $$T$$ if $$n = 3$$:
$$T = 2(3) + 1 = 6 + 1 = 7$$
(b) Find $$T$$ if $$n = -4$$:
$$T = 2(-4) + 1 = -8 + 1 = -7$$
(c) Find $$n$$ if $$T = 7$$:
Set up equation: $$7 = 2n + 1$$
Subtract 1: $$7 - 1 = 2n$$
$$6 = 2n$$
Divide both sides by 2:
$$\frac{6}{\cancel{2}} = \frac{2n}{\cancel{2}}$$
$$3 = n$$
(d) Find $$n$$ if $$T = 21$$:
Set up equation: $$21 = 2n + 1$$
Subtract 1: $$21 - 1 = 2n$$
$$20 = 2n$$
Divide both sides by 2:
$$\frac{20}{\cancel{2}} = \frac{2n}{\cancel{2}}$$
$$10 = n$$
3. Consider the formula $$v = 5 - 3r$$.
(a) Find $$v$$ if $$r = 5$$:
$$v = 5 - 3(5) = 5 - 15 = -10$$
(b) Find $$r$$ if $$v = 17$$:
Set up equation: $$17 = 5 - 3r$$
Subtract 5: $$17 - 5 = -3r$$
$$12 = -3r$$
Divide both sides by -3:
$$\frac{12}{\cancel{-3}} = \frac{-3r}{\cancel{-3}}$$
$$-4 = r$$
(c) Find $$r$$ if $$v = 25$$:
Set up equation: $$25 = 5 - 3r$$
Subtract 5: $$25 - 5 = -3r$$
$$20 = -3r$$
Divide both sides by -3:
$$\frac{20}{\cancel{-3}} = \frac{-3r}{\cancel{-3}}$$
$$-\frac{20}{3} = r$$
4. Consider the rule $$A = q + 4$$.
(a) Find $$A$$ if $$q = 3$$:
$$A = 3 + 4 = 7$$
(b) Find $$q$$ if $$A = 5$$:
Set up equation: $$5 = q + 4$$
Subtract 4: $$5 - 4 = q$$
$$1 = q$$
(c) Find $$A$$ if $$A = 3$$ and $$q = 3$$:
This is a given value, so $$A = 3$$
5. Consider the formula $$G = 7x + 2y$$.
(a) Find $$G$$ if $$x = 3$$ and $$y = 1$$:
$$G = 7(3) + 2(1) = 21 + 2 = 23$$
(b) Find $$x$$ if $$G = 11$$ and $$y = 3$$:
Set up equation: $$11 = 7x + 2(3)$$
Simplify: $$11 = 7x + 6$$
Subtract 6: $$11 - 6 = 7x$$
$$5 = 7x$$
Divide both sides by 7:
$$\frac{5}{\cancel{7}} = \frac{7x}{\cancel{7}}$$
$$\frac{5}{7} = x$$
(c) Find $$y$$ if $$G = 31$$ and $$x = 3$$:
Set up equation: $$31 = 7(3) + 2y$$
Simplify: $$31 = 21 + 2y$$
Subtract 21: $$31 - 21 = 2y$$
$$10 = 2y$$
Divide both sides by 2:
$$\frac{10}{\cancel{2}} = \frac{2y}{\cancel{2}}$$
$$5 = y$$