Answer:
Before you get started, take this readiness quiz.
Is n÷5 an expression or an equation? If you missed this problem, review Example 2.1.4.
Simplify 45. If you missed this problem, review Example 2.1.6.
Simplify 1+8•9. If you missed this problem, review Example 2.1.8.
Evaluate Algebraic Expressions
In the last section, we simplified expressions using the order of operations. In this section, we’ll evaluate expressions—again following the order of operations.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
Example 2.3.1: evaluate
Evaluate x+7 when
x=3
x=12
Solution
To evaluate, substitute 3 for x in the expression, and then simplify.
x+7
Substitute.
3+7
Add.
10
When x=3, the expression x+7 has a value of 10.
To evaluate, substitute 12 for x in the expression, and then simplify.
x+7
Substitute.
12+7
Add.
19
When x=12, the expression x+7 has a value of 19. Notice that we got different results for parts (a) and (b) even though we started with the same expression. This is because the values used for x were different. When we evaluate an expression, the value varies depending on the value used for the variable.
exercise 2.3.1
Evaluate: y+4 when
y=6
y=15
Answer a
Answer b
exercise 2.3.2
Evaluate: a−5 when
a=9
a=17
Answer a
Answer b
Example 2.3.2
Evaluate 9x−2, when
x=5
x=1
Solution
Remember ab means a times b, so 9x means 9 times x.
To evaluate the expression when x=5, we substitute 5 for x, and then simplify.
9x−2
Substitute 5 for x.
9⋅5−2
Multiply.
45−2
Subtract.
43
To evaluate the expression when x=1, we substitute 1 for x, and then simplify.
9x−2
Substitute 1 for x.
9⋅1−2
Multiply.
9−2
Subtract.
7
Notice that in part (a) that we wrote 9•5 and in part (b) we wrote 9(1). Both the dot and the parentheses tell us to multiply.
exercise 2.3.3
Evaluate: 8x−3, when
x=2
x=1
Answer a
Answer b
exercise 2.3.4
Evaluate: 4y−4, when
y=3
y=5
Answer a
Answer b
Example 2.3.3: evaluate
Evaluate x2 when x=10.
Solution
We substitute 10 for x, and then simplify the expression.
x2
Substitute 10 for x.
102
Use the definition of exponent.
Evaluate: 2x when x=6.
Answer
exercise 2.3.8
Evaluate: 3x when x=4.
Answer
Example 2.3.5: evaluate
Evaluate 3x+4y−6 when x=10 and y=2.
Solution
This expression contains two variables, so we must make two substitutions.
3x+4y−6
Substitute 10 for x and 2 for y.
3(10)+4(2)−6
Multiply.
30+8−6
Add and subtract left to right.
32
When x=10 and y=2, the expression 3x+4y−6 has a value of 32.
exercise 2.3.9
Evaluate: 2x+5y−4 when x=11 and y=3
Answer
exercise 2.3.10
Evaluate: 5x−2y−9 when x=7 and y=8
Answer
Example 2.3.6: evaluate
Evaluate 2x2+3x+8 when x=4.
Solution
We need to be careful when an expression has a variable with an exponent. In this expression, 2x2 means 2•x•x and is different from the expression (2x)2, which means 2x•2x.
2x2+3x+8
Substitute 4 for each x.
2(4)2+3(4)+8
Simplify 42.
2(16)+3(4)+8
Multiply.
32+12+8
Add.
52
exercise 2.3.11
Evaluate: 3x2+4x+1 when x=3.
Answer
exercise 2.3.12
Evaluate: 6x2−4x−7 when x=2.
Answer
Identify Terms, Coefficients, and Like Terms
Algebraic expressions are made up of terms. A term is a constant or the product of a constant and one or more variables. Some examples of terms are 7, y, 5x2, 9a, and 13xy.