Algebra 1 Notes SOL A.4 Equations Mrs. Grieser - Loudoun County Public ...
Algebra 1 Notes SOL A.4 Equations
Mrs. Grieser
Name: __________________________________________ Date: _______________ Block: _______
Equations An equation is an open sentence where two expressions are set _____________.
Equations may have one or more unknowns (_______________) which we may try to solve.
Solving an equation means finding the value(s) of variable(s) that make the equation ____________.
Equations that have the same solution(s) are called ____________________.
We use ______________________ operations to solve equations.
We justify the steps in solving equations by using field properties.
Solving Equations "Isolate" the variable, justifying steps using field properties (properties of equality):
1) Put variables on one side of the = and numbers on the other by isolating x:
perform inverse operations (add, subtract, multiply, or divide)
2) Whatever you do to one side of the equation, you do to the other
3) Verify solutions
substitute solution in original equation (DO NOT SKIP THIS STEP!!!!!!) S
Field Properties of Equality:
Property of Equality Reflexive Property of Equality
Algebra (for real numbers a, b, c) a = a
Example
Symmetric Property of Equality If a = b, then b = a
Transitive Property of Equality If a = b and b = c, then a = c
Substitution Property of Equality If a = b, then a can be substituted for b
Addition Property of Equality
If a = b, then a + c = b + c
Subtraction Property of Equality If a = b, then a ? c = b - c
Multiplication Property of Equality
Division Property of Equality
If a = b, then ac = bc If a = b and c 0, then a b
cc
Algebra 1 Notes SOL A.4 Equations
Solve the equations:
a) x ? 4 = 6
x ? 4 + 4 = 6 + 4 x = 10 VERIFY: Is 10 a solution? (10) ? 4 = 6
6=6
b) x + 3 = -5
x + 3 ? 3 = -5 ? 3 x = -8 VERIFY: Is -8 a solution? (-8) + 3 = -5
-5 = -5
Mrs. Grieser Page 2
c) 4x = 16 4x ? 4 = 16 ? 4 x = 4 VERIFY: Is 4 a solution? 4(4) = 16 16 = 16
Solve the equations, justifying steps:
a) Solve x + 4 = 10 1) x + 4 = 10 2) x + 4 ? 4 = 10 ? 4
3) x = 6
Given Subtraction Property of Equality Simplify
b) Solve 2 x = 4 3
1) 2 x = 4 3
Given
2) 3 2 x 3 4 Mult. Property of Equality 23 2
3) x = 6
Simplify
Two-Step Equations
SAME! Put variables on one side of the = and numbers on the other:
How to Solve Two-Step Equations 1) Clear parentheses (distribute) and combine like terms if necessary 2) Do add/subtract steps first
3) Do multiply/divide steps
Examples:
a) 5x + 9 = 24
5x + 9 ? 9 = 24 ? 9 __________________
5x = 15
__________________
5x 15 55
__________________
x = 3
__________________
VERIFY:
b) x 5 11 2
x 5 5 11 5 ________________ 2
x 16 2
________________
2 x 216 2
________________
x = 32
_________________
VERIFY:
c) 3x + 2x = 15
d) 4(x - 6) = 32
VERIFY:
VERIFY:
Algebra 1 Notes SOL A.4 Equations
Mrs. Grieser Page 3
Practice - solve the equations, justifying steps with field properties:
a) x + 9 = 25
b) -4x = -20
c) 3 x 3 5
d) 2x + 3 = -9
e) a 4 6 3
f) -1 = z 3 37
g) 7x ? 4x = 21
h) 3(x + 2) = 9
Multistep Equations and Equations with Variables on Both Sides
How to Solve Multi-Step Equations and Equations with Variables on Both Sides 1) Clear parentheses (distribute) and combine like terms if necessary 2) Add/subtract variable terms so that variable is on one side (NEW STEP!) 3) Do add/subtract steps first 4) Do multiply/divide steps
Example: Solve 7 ? 3x = 4x ? 7
1) 7 ? 3x = 4x ? 7 2) 7 ? 3x - 4x = 4x ? 7 - 4x 3) 7 ? 7x = - 7 4) 7 -7x - 7 = -7 - 7
Given ________________________________________________ ________________________________________________ ________________________________________________
5) -7x = -14 6) - 7x -14
7 -7 7) x = 2
________________________________________________ ________________________________________________
________________________________________________
Examples: Solve the equation, justifying steps...
a) 9x ? 5 = 1 (16x + 60) 4
b) 3(x + 12) ? x = 4(2 ? x) ? 3x + 2x
9x ? 5 = 4x + 15 ______________________
5x ? 5 = 15
______________________
5x = 20
______________________
x = 4
_____________________
Algebra 1 Notes SOL A.4 Equations
Special cases:
Identity case (solutions are all real numbers):
2x + 6 = 2(x + 3)
2x + 6 = 2x + 6 Distribute
0 = 0
Subtraction Prop. of =
Where did the variable go??
When we get a TRUE statement at the end when the variable "disappears," EVERY x is a solution (the two sides of the equation are identical!).
ALL REAL NUMBERS are solutions.
Mrs. Grieser Page 4
No solution case:
3x = 3(x + 4)
3x = 3x + 12 Distribute
0 = 12
Subtraction Prop. of =
Where did the variable go??
When we get a FALSE statement at the end when the variable "disappears," there are NO SOLUTIONS. There is no value of x that makes the equation true.
Other Equations: Solve: a) x 3
42
b) x 2 x 1 3
Cross Product Property: If a c then ad = bc bd
REMEMBER TO GROUP NUMERATORS AND DENOMINATORS (use parentheses)
You Try: Solve the equation if possible; if not, write "all real numbers" or "no solution"...
a) 8x + 5 = 6x + 1
b) x + 1 = 3x - 1
c) 9x = 6(x + 4)
d) 7(x + 7) = 5x + 59
e) 2 ? 15x = 5(-3x + 2)
f) 12y + 6 = 6(2y + 1)
g) 5(x + 2) = 3 (5 + 10x) 5
h) 40 + 14x = 2(-4x ? 13)
i) 2(3x + 2) = 1 (12x + 8) 2
j) x 9 23
k) 4 8 x-8 2
l) 2 x 5 21- x
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- 6 1 solving inequalities in one variables kyrene school district
- solving equations in one variable san juan unified school district
- literal equations kuta software
- solving equations a co teaching lesson plan virginia
- integrated algebra a lancaster high school
- supporting students understanding of linear equations with one ed
- mathematics instructional plan solving linear inequalities in one variable
- unit 1 equations and inequalities algebra 1 long beach unified school
- solving linear equations in one variable
- 2 5 solving for a variable rochester city school district
Related searches
- biology form 1 notes pdf
- solve 4 equations 4 unknowns
- 4 equations 4 unknowns
- algebra 1 notes pdf
- form 1 notes for free
- loudoun county jury duty rules
- algebra 1 4 2 worksheet answer
- 4 equations 4 unknowns solver
- biology 1 notes pdf
- psychology chapter 1 notes pdf
- computer application 1 notes pdf
- 4 equations 3 unknowns calculator