Transcript Solving One-Step Equations by Adding

Chapter 3.2 and 3.3 –
Solving One-Step
Equations
An equation is a mathematical statement that
two expressions are equal.
A solution of an equation is a value of the
variable that makes the equation true. A
solution set is the set of all solutions. Finding
the solutions of an equation is also called solving
the equation.
To find solutions, perform inverse operations
until you have isolated the variable. A
variable is isolated when it appears by itself on
one side of an equation, and not at all on the
other side.
Inverse Operations
Add x.
Multiply by x.
Subtract x.
Divide by x.
An equation is like a balanced scale. To keep the
balance, you must perform the same inverse
operation on both sides of the equation.
Example 1 - Solve the equation and then check
your solution.
y – 8 = 24
+8
Since 8 is subtracted from
y, add 8 to both sides to
undo the subtraction.
+8
y = 32
Check
y – 8 = 24
32 – 8
24
24
24
To check your solution,
substitute 32 for y in the
original equation.
Example 2 - Solve the equation and then check
your solution.
4.2 = t + 1.8
–1.8
–1.8
2.4 = t
Check 4.2 = t + 1.8
4.2 2.4 + 1.8
4.2 4.2 
Since 1.8 is added to t,
subtract 1.8 from both sides
to undo the addition.
To check your solution,
substitute 2.4 for t in the
original equation.
Example 3 - Solve the equation. Check your
answer.
–6 = k – 6
+6
+6
0=k
Check
–6 = k – 6
–6 0 – 6
–6 –6 
Since 6 is subtracted from
k, add 6 to both sides
to undo the subtraction.
To check your solution,
substitute 0 for k in the
original equation.
Example 4 - Solve the equation. Check your
answer.
–24 = –6v
-6
-6
4=v
Check
–24 = –6v
–24 –6(4)
–24
–24 
Since v is multiplied by –6,
divide both sides by –6 to
undo the multiplication.
To check your solution,
substitute 4 for v in the
original equation.
Example 5 - Solve the equation. Check your
answer.
Since j is divided by 3,
multiply from both
sides by 3 to undo the
division.
–24 = j
Check
To check your solution, substitute
–24 for j in the original equation.
–8
–8 
Example 6 - Solve each equation. Check your
answer.
0.5y = –10
Since y is multiplied by 0.5,
divide both sides by 0.5 to
undo the multiplication.
y = –20
0.5y = –10
Check
0.5(–20) –10
–10
–10 
To check your solution,
substitute –20 for y in the
original equation.
Example 7 - Solve each equation. Then check
your solution.
The reciprocal of
is
w is multiplied by
both sides by
Check :
5
, ( 24)  20
6
. Since
multiply
.
, -20 = -20
Example 8 - Solve the equation. Check your
answer.
The reciprocal of
is
w is multiplied by
both sides by
. Since
multiply
.
w = 612
Check
102
102 
To check your solution,
substitute 612 for w in the
original equation.
Additional Example 9: Application
Ciro deposits 1
of the money he earns from
4
mowing lawns into a college education fund. This
year Ciro added $285 to his college education
fund. Write and solve an equation to find out how
much money Ciro earned mowing lawns this year.
Additional Example 9 Continued
1
4
times

earnings
e
is
$285
=
$285
Write an equation to represent the
relationship.
4
1
4
1  4 e = 1  285
e = $1140
1
4
The reciprocal of 4 is 1 . Since e
is multiplied by 1 ,
4
multiply both sides by 4 .
1
The original earnings were $1140 .
Tricky Problems
Solve and check each equation
a.) f + (-14) = 10
x = 24
b.) y – (– 1.3) = 2.4
y = 1.1
a 15
c.)

3 9
a=5
Chapter 3.2 and 3.3 Review…Solve and
check each equation
1.) (– 3) + x = 10
2.) y – (–2.4) = 8.5
x = 13
3.) – 7a = 56
a = -8
y = 6.1
4.)
2
x  8
3
x = -12
Assignment
• Worksheet 3-2 & 3-3 (Front & Back) (In-Class)
• Page 132 #’s 15-35 (odd), 43-45 (all) (Homework)
• Pages 138-139 #’s 13-31 (odd), 33-35 (all)
(Homework)
• (Make sure you WRITE out the problem
and SHOW ALL YOUR WORK to receive full
credit!!!)