VOCABULARY distributive property-multiply the outside term by all terms on the inside of the parenthesis expression-numeral and/or variable joined by any combination of the four basic operationslike terms-two or more terms that have the same variables and powerscommutative property-the property that changes the order of somethingequation-a mathematical statement that two expressions are equal monomial-a number multiplied by one or more variables coefficient-the number that is multiplied by one or more variables inductive reasoning-using examples and non-examples to identify a pattern and make a decision combining like terms-they have to have the same variables and exponents the sign to the left is the sign you use when adding and subtracting
Key Terms
-combining like terms
-simplifying larger expressions
-solving two step equations
-writing equations for word problems
Simplify usually means two things: -Distribute -Combining Like Terms
Suggestions:
1)Simplify each side of the equal sign separately first
2)Move all the variables to the left of the equal sign
Also, use a two column format to explain the steps you took when solving a 2 step equation.
Examples of two step equations and how to solve them:
5x+14=29
write out what you would do first(P.E.M.D.A.S.)
multiply by 5 29-14=15
add 14 15/5=3 x=3
then work from the bottom of the list and go up makinig sure you are doing the opposite of what it's telling you to do
you can also use the two column format to explain how you got your answer
Writing Equations for Word Problems Tips for Word Problems 1.)Read the entire problem 2.)Think about what is going on in the problem. Imagine yourself in the situation. 3.)Identify what changes or what is missing and assign a variable to represent it 4.)Circle numbers and words that clue you into the operation 5.)Create an algebraic expression of the problem using your clue words 6.)Solve the equation 7.)Check to make sure your answer makes sense
Key Words addition-and,plus,sum,more than,increased by,total,in all subtraction-minus,difference,less than,subtract,decreased by multiplication-times,product,multiplied,each,per,of division-divided,quotient,cut in half
Solving Inequalities
What is an inequality?
A term used to compare the size of 2 quatities
Four Signs:
< less than
>greater than
<-less than or equal to
>-greater than or equal to
= with a slash-not equal
Special Rules:
If you multiply or divide by a NEGATIVE, then you flip then inequality symbol at the end.
Solving Equations with variables on BOTH sides of the equal sign When variables are on both sides: 1.) Simplify each side by distributing and combining like terms.
2.) Multiply ALL terms by the lowest common dinominator to get rid of fractions.
3.) Based on the sign to the left of the variable, add or subtract one of the variable terms to move it across the equal sign. WORK BACKWARDS!!!!!!
example:3e-2-9e+3+4e=5e+7-e
First-combine like terms:3e-2-9e+3+4e=5e+7-e
-2e+1=4e+7
Next-move all variables to the left(in this case, subtract 4 from both sides)
-2e+1=4e+7
-4e -4e
you get:-6e+1=7
Last-work backwards
-6e+1=7 multiply -6
add 1
7-1=6/-6=-1 SO:e=-1
distributive property-multiply the outside term by all terms on the inside of the parenthesis
expression-numeral and/or variable joined by any combination of the four basic operationslike terms-two or more terms that have the same variables and powerscommutative property-the property that changes the order of somethingequation-a mathematical statement that two expressions are equal
monomial-a number multiplied by one or more variables
coefficient-the number that is multiplied by one or more variables
inductive reasoning-using examples and non-examples to identify a pattern and make a decision
combining like terms-they have to have the same variables and exponents the sign to the left is the sign you use when adding and subtracting
Key Terms
-combining like terms
-simplifying larger expressions
-solving two step equations
-writing equations for word problems
Solving 2 Step Equations
What's the key to solving equations??
WORKING BACKWARDS!
Seriously-SimplifyAunt-Add
Sally-Subtract
My-Multiply
Dear-Divide
Excuse-Exponents
Please-Parenthesis
Simplify usually means two things:
-Distribute
-Combining Like Terms
Suggestions:
1)Simplify each side of the equal sign separately first
2)Move all the variables to the left of the equal sign
Also, use a two column format to explain the steps you took when solving a 2 step equation.
Examples of two step equations and how to solve them:
5x+14=29
write out what you would do first(P.E.M.D.A.S.)
multiply by 5 29-14=15
add 14 15/5=3 x=3
then work from the bottom of the list and go up makinig sure you are doing the opposite of what it's telling you to do
you can also use the two column format to explain how you got your answer
Writing Equations for Word Problems
Tips for Word Problems
1.)Read the entire problem
2.)Think about what is going on in the problem. Imagine yourself in the situation.
3.)Identify what changes or what is missing and assign a variable to represent it
4.)Circle numbers and words that clue you into the operation
5.)Create an algebraic expression of the problem using your clue words
6.)Solve the equation
7.)Check to make sure your answer makes sense
Key Words
addition-and,plus,sum,more than,increased by,total,in all
subtraction-minus,difference,less than,subtract,decreased by
multiplication-times,product,multiplied,each,per,of
division-divided,quotient,cut in half
Solving Inequalities
What is an inequality?A term used to compare the size of 2 quatities
Four Signs:
< less than
>greater than
<-less than or equal to
>-greater than or equal to
= with a slash-not equal
Special Rules:
If you multiply or divide by a NEGATIVE, then you flip then inequality symbol at the end.
Solving Equations with variables on BOTH sides of the equal sign
When variables are on both sides: 1.) Simplify each side by distributing and combining like terms.
2.) Multiply ALL terms by the lowest common dinominator to get rid of fractions.
3.) Based on the sign to the left of the variable, add or subtract one of the variable terms to move it across the equal sign.
WORK BACKWARDS!!!!!!
example:3e-2-9e+3+4e=5e+7-e
First-combine like terms:3e-2-9e+3+4e=5e+7-e
-2e+1=4e+7
Next-move all variables to the left(in this case, subtract 4 from both sides)
-2e+1=4e+7
-4e -4e
you get:-6e+1=7
Last-work backwards
-6e+1=7 multiply -6
add 1
7-1=6/-6=-1
SO: e=-1
Resources**
-http://www.google.com/url
we used this website to find the definitions
-http://www.hsunlimited.com/worksheets/createworksheet.php
http://www.kutasoftware.com/free.html
at these two websites you can find worksheets to practice two step equations and almost everything that we will learn in unit 2(including combining like terms)
http://www.math-play.com/Two-Step-Equations-Game.html
http://www.algebrahelp.com/
these websites have games you can play to practice solving two step equations and you can take lessons on what we are learning, practice with worksheets, and more!
http://www.yourteacher.com/
this will help you solve two step equations and many more by searching it on the website!
http://www.algebra-class.com/algebra-equations.html
here you read lessons and practice skills we are learning by looking at examples in a two column format like we did in class
http://www.cosmeo.com/bysubject.cfm?math
here you can play games and watch videos to help you solve equations
http://regentsprep.org/Regents/math/ALGEBRA/AE2/LSolvEq.htm
here they give you examples and go step by step on how to solve them