(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
- (a) (b)
(c) - 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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