Beginning Algebra, 11th Edition

(Marvins-Underground-K-12) #1

(c) A number subtractedfrom 12


12 - x


24 CHAPTER 1 The Real Number System


NOW TRY
EXERCISE 3
Write each word phrase as an
algebraic expression, using x
as the variable.


(a)The sum of a number and 10


(b)A number divided by 7


(c)The product of 3 and the
difference between 9 and a
number


NOW TRY ANSWERS



  1. (a) (b)
    (c)

  2. yes


319 - x 2

x
x+10, or 10+x 7

Be careful with order.

Compare this result with “12 subtracted from a number,” which is


(d)The productof 11 and a number


(e) 5 divided bya number


or


5


x


5 ,x,


11 #x, or 11 x


x-12.


5 xis notcorrect here.

(f )The product of2 and the differencebetween a number and 8


We are multiplying 2 times “something.” This “something” is the difference


between a number and 8, written We use parentheses around this difference.


2 # 1 x- 82 , or 21 x- 82


x- 8.


, which means the difference
between 8 and a number, is not correct.

8 - x

NOW TRY

OBJECTIVE 3 Identify solutions of equations.An equationis a statement


that two algebraic expressions are equal. An equation always includes the equality


symbol,.


z^2 =4, 41 m- 0.5 2 = 2 m


3


4


x+


1


2


= 0,


x+ 4 = 11, 2 y=16, 4 p+ 1 = 25 - p,





To solvean equation means to find the values of the variable that make the equation


true. Such values of the variable are called the solutionsof the equation.


Deciding Whether a Number Is a Solution of an Equation

Decide whether the given number is a solution of the equation.


(a) ;7


Let
Multiply.

✓True—the left side of the equation


equals the right side.

36 = 36


35 + 1  36


5 # 7 + 1  36 p=7.


5 p+ 1 = 36


5 p+ 1 = 36


EXAMPLE 4

⎧Equations



NOW TRY
EXERCISE 4
Decide whether the given
number is a solution of the
equation.


8 k+ 5 =61; 7


Be careful!
Multiply first.

The number 7 is a solution of the equation.


(b) ;4


Let
Multiply.
False—the left side does not
equal the right side.

The number 4 is not a solution of the equation. NOW TRY


30 = 32


36 - 6  32


9 # 4 - 6  32 m=4.


9 m- 6 = 32


9 m- 6 = 32


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