Transcript Ch 1-7 Solving Equations by Adding or Subtracting

1-7 Solving Equations by Adding or Subtracting
Evaluating
Algebraic Expressions
California
Standards
Preparation for
AF4.0
Students solve simple linear equations and
inequalities over the rational numbers.
AF1.4 Use algebraic terminology (e.g.,
variable, equation, term, coefficient, inequality,
expression, constant) correctly.
1-7 Solving Equations by Adding or Subtracting
Evaluating
Algebraic
Expressions
An equation
is a mathematical
sentence
that
uses an equal sign to show that two expressions
have the same value. All of these are equations.
3 + 8 = 11
r + 6 = 14
–24 = x – 7
–100
= 50
2
To solve an equation that contains a variable, find
the value of the variable that makes the equation
true. This value of the variable is called the
solution of the equation.
1-7 Solving Equations by Adding or Subtracting
Evaluating
Algebraic
Adding
and subtracting
by the sameExpressions
number are
inverse operations. Inverse operations “undo” each
other. To solve an equation, use inverse operations to
isolate the variable. In other words, get the variable
alone on one side of the equal sign.
The properties of equality allow you to perform
inverse operations. These properties show that you
can perform the same operation on both sides of an
equation.
1-7 Solving Equations by Adding or Subtracting
Additional Example 2A: Solving Equations Using
Addition and Subtraction Properties
Evaluating Algebraic Expressions
Solve.
10 + n = 18
10 + n = 18
–10
–10
0+n= 8
n= 8
Check
10 + n = 18
?
10 + 8 = 18
?
18 = 18 
Since 10 is added to n, subtract 10
from both sides to undo the addition.
Identity Property of Addition: 0 + n = n.
To check your solution, substitute 8 for n
in the original equation.
1-7 Solving Equations by Adding or Subtracting
Additional Example 2B: Solving Equations Using
Addition and Subtraction Properties
Evaluating Algebraic Expressions
Solve.
p–8=9
p–8=9
+8 +8
p + 0 = 17
p = 17
Check
p–8=9
?
17 – 8 = 9
?
9 = 9
Since 8 is subtracted from p, add 8 to
both sides to undo the subtraction.
Identity Property of Addition: p + 0 = p.
To check your solution, substitute 17 for p
in the original equation.
1-7 Solving Equations by Adding or Subtracting
Additional Example 2C: Solving Equations Using
Addition and Subtraction Properties
Evaluating Algebraic Expressions
Solve.
22 = y – 11
22 = y – 11
+ 11
+ 11
Since 11 is subtracted from y, add 11
to both sides to undo the subtraction.
33 = y + 0
33 = y
Identity Property of Addition: y + 0 = y.
Check
22 = y – 11 To check your solution, substitute 33 for y
?
22 = 33 – 11 in the original equation.
?
22 = 22 
1-7 Solving Equations by Adding or Subtracting
Evaluating Algebraic Expressions