Beginning Algebra, 11th Edition

OBJECTIVE 4 Identify solutions of equations from a set of numbers.A setis

a collection of objects. In mathematics, these objects are most often numbers. The objects

that belong to the set, called elementsof the set, are written between braces.

The set containing the numbers 1, 2, 3, 4, and 5

Finding a Solution from a Given Set

Write each word statement as an equation. Use xas the variable. Then find all solu-

tions of the equation from the set

(a)The sum of a number and four is six.

The sum of

a number and four is six.

x+ 4 = 6

5 0, 2, 4, 6, 8, 10 6.

EXAMPLE 5

5 1, 2, 3, 4, 5 6

SECTION 1.3 Variables, Expressions, and Equations 25

NOW TRY
EXERCISE 5
Write the word statement as
an equation. Then find all
solutions of the equation from
the set

The sum of a number and

nine is equal to the difference

between 25 and the number.

5 0, 2, 4, 6, 8, 10 6.

NOW TRY ANSWERS

5. ; 8


6. (a)equation (b)expression

x+ 9 = 25 - x

Use xfor the

unknown number.

One by one, mentally substitute each number from the given set in

Since is true, 2 is the only solution.

(b)Nine more than five times a number is 49.

Start with 5x, and The word is

then add 9 to it. translates as

Substitute each of the given numbers. The solution is 8 , since is true.

(c) The sum of a number and 12 is equal to four times the number.

The sum of a is four times

number and 12 equal to the number.

Substituting each of the given numbers in the equation leads to a true statement only

for since is true. NOW TRY

OBJECTIVE 5 Distinguish between expressionsand equations.Students

often have trouble distinguishing between equations and expressions. An equation is

a sentence—it has something on the left side, an symbol, and something on the

right side. An expression is a phrase that represents a number.

Left side Right side

Equation Expression

(to solve) (to simplify or evaluate)

4 x+ 5 = 9 4 x+ 5



x= 4 , 4 + 12 = 4142

x+ 12 = 4 x

5 # 8 + 9 = 49

5 x+ 9 = 49 5 #x= 5 x

=.

x+ 4 =6. 2 + 4 = 6

5 0, 2, 4, 6, 8, 10 6

⎧⎨⎩ {

Distinguishing between Equations and Expressions

Decide whether each of the following is an equationor an expression.

(a) There is no equals symbol. This is an expression.

(b) There is an equals symbol with something on either side of it.

This is an equation. NOW TRY

2 x= 5 y

2 x- 5 y

EXAMPLE 6

NOW TRY
EXERCISE 6
Decide whether each of the
following is an expressionor
an equation.

(a)

(b) 2 x+ 5 - 6

2 x+ 5 = 6

The word is

translates as .=