11.1

Determining Whether Values Are Solutions

An equation is a mathematical statement that two expressions are equal. An
equation may or may not contain variables. For an equation that contains a
variable, a solution of the equation is a value of the variable that makes the
equation true.

Expression

Equation

Numerical

5 + 4

5 + 4 = 9

Words

A number plus 4

A number plus 4 is 9

Algebraic

n + 4

n + 4 = 9

An expression
represents a single
value

An equation represents
a relationship between
two values

An equation relates two expressions
using a symbol for “is” or “equals”

Determine whether the given value is a solution of the equation.

x + 9 = 15; x = 6

?

6 + 9 = 15

?

15 = 15

Multiple Choice

11 = n + 6; n = 5

• Yes

• no

Multiple Choice

y - 6 = 24; y = 18

• yes

• no

Multiple Choice

x/9 = 4; x = 36

• yes

• no

Multiple Choice

15t = 100; t = 6

• yes

• no

Writing Equations to Represent Situations

You can represent some real-world situations with an equation. Making a model first can help you organize the information and identify what the variable represents.

​17 + p = 46

Mark scored 17 points for the home team in a basketball game. His teammates as a group scored p points. Write an equation to represent this situation.

​

​

​

Mark's + Teammates's = Total points

points points

P

represnts

the number

of points Mark's teammates scored

Multiple Choice

The sum of a number f and 9 is equal to 38.

• f - 9 = 38

• 9f = 38

• f + 9 = 38

• 38 - 9 = f

Multiple Choice

The product of 17 and a number n is equal to 102.

• 17 + n = 102

• 102n = 17

• 17 - n = 102

• 17n = 102

Multiple Choice

Craig is c years old. His 12-year-old friend Kaitlin is 1/2 year younger than Craig.

• c - 1/2 = 12

• c + 1/2 = 12

• c/2 = 12

• 12/c = 2