Transcript Introduction to Algebra - Gertz

Do Now
Complete in your lecture notebook quietly.
1) 4x + 18 is an example of what vocabulary
word?
2) Which operation should be performed first
in the expression 4 + (8 ÷2) x 3 – 10?
3) Simplify 27 ÷ 3 + (12 – 4)
4) What property does the equation
( x + y ) + z = x + (y + z) represent?
5) What property is shown by the equation
5 + (3 + 6) = 5 + (6 + 3)?
Solving ONE STEP
EQUATIONS
Objective
Students will be able to:
demonstrate their understanding of
inverse operations by correctly solving 4
one-step equations at a basic level of
proficiency.
Preparation for Standard 5.0 Students
solve multi-step problems, including word
problems, involving linear equations and
linear inequalities in one variable and
provide justification for each step.
Think of an equation as a balance scale.
Whatever you do to one side has to be done
to the other to keep it balanced!
ONE STEP EQUATIONS
To solve one step equations, you need
to ask three questions about the
equation:
• What is the variable?
• What operation is performed on the variable?
• What is the inverse operation?
(The one that will undo what is being
done to the variable)
ONE STEP EQUATIONS
Vocabulary
• The addition property of equality tells us to
add the same thing on both sides to keep the
equation equal.
• The subtraction property of equality tells us
to subtract the same thing on both sides to
keep the equation equal.
ONE STEP EQUATIONS
Vocabulary
• The multiplication property of equality tells
us to multiply the same thing on both sides to
keep the equation equal.
• The division property of equality tells us to
divide the same thing on both sides to keep the
equation equal.
ONE STEP EQUATIONS
Example 1 Solve x + 4 = 12
ONE STEP EQUATIONS
Example 2 Solve y - 7 = -13
ONE STEP EQUATIONS
Example 3 Solve –6a = 12
ONE STEP EQUATIONS
b = -10
Example 4 Solve 2
When solving equations, we want to eliminate
double signs.
y + (-3) = 8
is rewritten as
y–3=8
p – (-5) = 6
is rewritten as
p+5=6
As a general rule, replace “+ (- )” with “–” and
“– (- )” with “+”. This will make things less
confusing in the future!
1) Solve x + 2 = -3
Get the variable by itself. What is your
first step?
2) Solve 8 = m - 3
3) Solve y + (-3) = 7
4) Solve. -x - (-2) = 1
5) Solve -y – (-3) = 7
6) Negative thirty-four times a number
equals 578. Find the number.
7) Solve –12b = 276
8) Solve 35t = 595
9) Solve 32 = –16c
10)
Exit Slip
Solve each equation. Show all your work.
1)d + 18 = -27
2 p 18
2) 3
3)-12 + a = -36
4)-17y = 391