Transcript Unit 1: Solving Equations in One Variable

Algebra I Unit 1: Solving Equations
in One Variable
Learning Goal: 1.4
Michelle A. O’Malley
8th Grade Math
League Academy of Communication Arts
Greenville, South Carolina
Unit 1: Learning Goal 1.4
• Students will solve one-, two- and multi-step
equations using the properties of real
numbers and the properties of equality to
justify the steps including real-world
situations; represent solution process using
concrete models.
Unit 1: Learning Goal 1.4 – Essential
Knowledge and Skills for Students
• The students will use problem solving, reasoning,
communication, connections and representation to:
– Using the properties of real numbers and the properties of equality,
and solve equations.
– Use concrete and pictorial models to represent and solve equations
– Justify the steps to the solutions using the properties of real
numbers and the properties of equality.
– Demonstrate an understanding that equivalent equations have the
same solution.
– Demonstrate and understanding that adding the same quantity to
each side of an equation produces an equivalent equation.
– Write equations that represent real-world applications and solve
using appropriate methods.
– Math/write a verbal statement that describes a given equation.
Unit 1: Learning Goal 1.4
Algebra I Standards: EA-4.7, EA-1.3, and EA-1.6
• EA-4.7 – Carry out procedures to solve linear
equations in one variable algebraically.
• EA-1.3 – Apply algebraic methods to solve
problems in real world contexts.
• EA-1.6 – Understand how algebraic
relationships can be represented in concrete
models, pictorial models, and diagrams.
Solving Equations by using
addition and subtraction
Solving Equations by using
addition and subtraction
Solving Equations by using
addition and subtraction
27
-0.8
8
Note: that when you have a term such as – c = -27 such as the
one above. The variable actually has a coefficient of -1.
Remember that the product of two negative numbers is positive
you can multiply each side of the equation by -1 so that your
answer is c = 27.
Solving Equations by using
addition and subtraction
Helpful Hints:
•If the same number is added or subtracted to each side of an equation,
then the result is an equivalent equation. Equivalent Equations have the
same solution.
•To Solve an equation means to find all values of the variable that make the
equation a true statement. One way to do this is to isolate the variable
having a coefficient of 1 on one side of the equation. You can sometimes do
this by using the Addition Property of Equality.
•Isolating Variables – when isolating variables it does not matter whether
the variable ends up on the right side or the left side of the equation. For
example, the solution of 8 = 15 + z is still -7, even though the final step may
be -7 = z.
Solving Equations by using
addition and subtraction
Click here to try and electronically
balance equations
Solving Equations by using
multiplication and division
Solving Equations by using
multiplication and division
Solving Equations by using
multiplication and division
-7d/ -7 = -84/-7
d = 12
6y/6 = 54/6
y=9
2.4f/2.4 = 21.6/2.4
f=9
22b/22 = 176/22
b=8
Solving Equations by using
multiplication and division
(-6)(p/-6) = (7/12)(-6)
p = -3 1/2
Change – 2 1/3 into – 7/3, which
is an improper fraction
(-3/7)(-7/3q) = (21)(-3/7)
q = -9
Solving Multi-Step Equations
Solving Multi-Step Equations
Solving Multi-Step Equations
10 – 7p = -18
-10
-10
-7p = -28
-7p / -7 = -28 / -7
p=4
- 1.9r + 9.3 = 15
- 9.3 = -9.3
-1.9r = 5.7
-1.9r / -1.9 = 5.7/-1.9
r = -3
Solving Multi-Step Equations
(4)- 6 = [(-2n-3)/4](4)
-24 = -2n-3
-3
-3
-21/ -2 = - 2n/-2
n = 10 1/2
(5)(t / 5 – 4)= - 10(5)
t – 20 = -50
+ 20 = + 20
t = -30
Solving Equations
with variable on each side
Solving Equations
with variable on each side
Solving Equations
with variable on each side
Steps for solving Equations:
Step 1: Use the Distributive Property to remove the grouping symbols.
Step 2: Simplify the expressions on each side of the equals sign.
Step 3: Use the Addition and/or Subtraction Properties of Equality to get
the variables on one side of the equals sign and the numbers without
variables on the other side of the equals sign.
Step 4: Simplify the expression on each side of the equals sign.
Step 5: Use the Multiplication or Division Property of Equality to solve.
•If the solution results in a false statement, there is no solution
of the equation.
•If the solution results in an identity, the solution is all numbers.
Solving Equations
with variable on each side
18 + 2n = 4n – 9
- 2n = - 2n
18 = 2n - 9
+9=
+9
27 / 2 = 2n /2
n = 13 1/2
10 - 2.7y = y + 9
-9
= -9
1 – 2.7 y = y
+ 2.7y = + 2.7y
1/3.7 = 3.7y/3.7
y = 1/3.7 or .27
Solving Equations
with variable on each side
11.1c – 2.4 = -8.3c + 6.4
+ 8.3 c = + 8.3 c
19.4 c – 2.4 = 6.4
+ 2.4 = + 2.4
19.4 c/19.4 = 8.8/19.4
c = 8.8/19.4 or 0.45
3 – 4x = 8x + 8
+ 4x = 4x
3 = 12x + 8
-8 =
-8
- 5/12 = 12x/12
x = -5/12
Work Cited
• Carter, John A., et. al. Glencoe Mathematics
Algebra I. New York: Glencoe/McGrawHill, 2003.
• Greenville County Schools Math Curriculum
Guide