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Bell Quiz
Objectives
• Solve one-step equations by addition and
subtraction.
New Concept
• An equation is a statement that uses an
equal sign to show that two quantities are
equal.
• A solution of an equation in on variable
is a value of the variable that makes the
equation true.
Example 1
Identifying Solutions
State whether the value of the variable is a
solution of the equation
x + 6 = 9 for x = 3
Example 2
Identifying Solutions
State whether the value of the variable is a
solution of the equation
x – 6 = 9 for x = 3
Lesson Practice
State whether the value of the variable is a
solution of the equation
h – 14 = 2 for h = 12
Lesson Practice
State whether the value of the variable is a
solution of the equation
–11 = j – 4 for j = – 7
Equivalent Equations
• An equation is like a balance scale.
• The scale remains balanced when the
same quantity is added to both sides, or
when the same quantity is subtracted from
both sides.
• An equivalent equation has the same
solution set.
Addition and Subtraction
Properties of Equality
• By adding or subtracting the same quantity
from both sides of an equation, each equation
remains equivalent to the original equation
• Furthermore, each side of the equation
remains balanced as the equation is solved.
• The Addition and Subtraction Properties of
Equality hold for every real number a, b, and
c.
Addition and Subtraction Properties of Equality
Addition Property of Equality
You can add the same number to both sides of an equation and the
statement will still be true.
Examples:
2=2
3+2=2+3
5=5
a=b
a+c=b+c
Subtraction Property of Equality
You can subtract the same number from both sides of an equation
and the statement will still be true.
Examples:
10 = 10
10 – 4 = 10 – 4
6=6
a=b
a–c=b–c
Inverse Operations
• An inverse operation is an operation that
undoes another.
• To solve an equation, isolate the variable
on one side of the equal sign by using
inverse operation
Inverse Operations
Addition <------------> Subtraction
Multiplication <------------> Division
Example 3
Solving Equations by Adding
Solve. Then check the solution.
x – 3 = 12
Example 4
Solving Equations by Adding
Solve. Then check the solution.
–15 = n – 8
Lesson Practice
Solve. Then check the solution.
x – 5 = 17
Lesson Practice
Solve. Then check the solution.
– 30 = m – 12
Example 5
Solving Equations by Subtracting
Solve. Then check the solution.
k + 7 = 13
Example 6
Solving Equations by Subtracting
Solve. Then check the solution.
–21 = p + 9
Lesson Practice
Solve. Then check the solution.
p + 3 = 37
Lesson Practice
Solve. Then check the solution.
–14 = y + 8
Example 7
Solve Fraction Equations by Adding or Subtracting
Solve.
1 = –3
x+
4
8
Lesson Practice
Solve.
1
1
d+4 =3
2
6
Example 8
Application: Weather
On January 10, 1911, the temperature in
Rapid City, South Dakota fell 47°F in 15
minutes. What was the temperature if it fell
to 8°F?
Lesson Practice
Sam took the same test twice. On the
second test he scored 87, which was 13
points higher than on the first test. What
was his first test score?