Exercise 8 Page 197 - 1. Section 4.1 - Core Connections Integrated I, 2013

a Looking at the equation, we can guess that dividing both sides of it by the common factor will make it simpler to solve. The common factor of

200,

50,

and

8000

50,

so let's divide both sides of the equation by

50 .

200 x + 50 = 8000

$LHS / 50 = RHS / 50$

\frac{2 0 0 x + 5 0}{5 0} = \frac{8 0 0 0}{5 0}

Write as a sum of fractions

\frac{2 0 0 x}{5 0} + \frac{5 0}{5 0} = \frac{8 0 0 0}{5 0}

Calculate quotient

4 x + 1 = 160

b To simplify the equation, we should change it into one without fractions. To do so, we should multiply it by the least common factor of

4 x

and

8,

the expression

8 x .

\frac{2 1}{4 x} + \frac{9}{8} = 2

$LHS \cdot 8 x = RHS \cdot 8 x$

8 x (\frac{2 1}{4 x} + \frac{9}{8}) = 8 x (2)

Distribute $8 x$

\frac{8 x ( 2 1 )}{4 x} + \frac{8 x ( 9 )}{8} = 8 x (2)

▼

Calculate quotient

$\frac{a}{b} = \frac{a / 4 x}{b / 4 x}$

\frac{2 ( 2 1 )}{1} + \frac{8 x ( 9 )}{8} = 8 x (2)

$\frac{a}{b} = \frac{a / 8}{b / 8}$

\frac{2 ( 2 1 )}{1} + \frac{x ( 9 )}{1} = 8 x (2)

$\frac{a}{1} = a$

2 (21) + x (9) = 8 x (2)