Algebra
Lesson 3-4:
Solving Multi-Step Equations
This section is going to teach you:
- How to solve problems by working them out backward.
- How to solve equations that involve more than one operation to evaluate.
Vocabulary:
- Work Backward One of the problem solving-strategies
- Multi-Step Equations An Equation with more than one operation to evaluate
- Consecutive Integers Integers found right beside eachother on a number line; in order.
- Number Theory The study of numbers and their relationships.
Examples:
Example of some consecutive integers: 3, 4, 5, 6.
Other problem solving strategies:
- draw a diagram
- make a table or chart
- make a model
- guess and check
- check for hidden assumptions
- use a graph
- solve a simpler (or similar) problem
- eliminate the possibilites
- look for a pattern
- act it out
- list the possibilites
- idetify the cubgoals
Examples of some problems from this section:
1.) Solve this problem by working backwards:
A number is divided by 5, and then the quotient is added to 3. The result is 25. What is the number.
n/5+3=25
2.) Solve this equation:
5n + 6 = -4
3.) Write an equation for this problem:
Find three consecutive odd integers whos sum is -30.
4.) Estimate this person's shoe size if "L" represents the length of the person's foot in inches, and the
expression 2L - 12 can be used to evaluate.
What is the approximate length of a person's foot if their shoe size is size 5? How about size 9? Size 7?
5.)Solve this equation
5.)Solve this equation
2c+c+12=78
3c+12=78
3c+12=78
-12 -12
3c/3=66/3
3c+12=78
-12 -12
3c/3=66/3
3c=66
c=22
6.)Solve this equation
x-29=98
+29 +29
x=127
c=22
6.)Solve this equation
x-29=98
+29 +29
x=127
Additional Information:
Did you know that equations can be used to estimate the age of an animal?! Now you do! An American alligator that was just born is about 8 inches in length, and these alligators grow about 12 inches a year. So the expression 8 + 12a represents the length in inches of an alligator that is a years old. Since 10 feet 4 inches equals 10 (12) + 4 or 124 inches, the equation 8 + 12a =124 can be used to estimate the age of any alligator. Notice that this equation involves more than one operation.
Online resources:
www.gomath.com/htdocs/ToGoSheet/Algebra/consecutive.html
http://www.phschool.com/iText/math/sample_chapter/Ch02/02-03/PH_Alg1_ch02-03_Obj1.html
http://www.mathkalusa.com/equations_1.html
Websites to try problems:http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_OneVariableMultiStep.xml
Pictures:
http://www.phschool.com/iText/math/sample_chapter/Ch02/02-03/PH_Alg1_ch02-03_Obj1.html
http://www.mathkalusa.com/equations_1.html
Websites to try problems:http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_OneVariableMultiStep.xml
This page by: ~DV~AR~CH~