Expanding the walls of our classroom. This is an interactive learning ecology for students and parents in our Algebra 2 class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.
Linear Equation in One Variable A linear equation in one variable can be written in the form Ax+B=C where a,b, and c are real numbers, with a not equal to 0.
Addition and Multiplication Properties of Equality Addition Property of Equality For all real numbers, A,B, and C, the equations A=B and A+C=B are equivalent. In words, the same number may be added to each side of an equation without changing the solution set,
Multiplication Property of Equality For all real numbers A and B, and for C not equal to 0, the equations A=B and AC=BC are equivalent. In words, each side of an equation may be multiplied by the same nonzero number without changing the solution set.
Solving a Linear Equation in One Variable Step 1. Clear Fractions. Eliminate any fractions by multiplying each side by at the least common denominator. Step 2. Simplify each side separately. Use the distributive property to clear parentheses and combine like terms as needed. Step 3. Isolate the variable terms on one side. Use the addition property to get all terms with variables on one side of the equation and all numbers on the other. Step 4. Isolate the variable. Use the multiplication property to get an equation with just the variable (with coefficient 1) on one side. Step 5. Check. Substitute the proposed solution into the original equation.
2.2: Formulas Solving for a Specified Variable Step 1. Transform so that all terms containing the specified variable are on one side of the equation and all terms without that variable are on the other side. Step 2. If necessary, use the distributive property to combine the terms with the specified variable. The result should be the product of a sum or difference and the variable. Step 3. Divide each side by the factor that is the coefficient of the specified variable.
Solving a Percent Problem Let a represent a partial amount of b, the base, or whole amount. Then the following formula can be used in solving a percent problem. amount/base = a/b = percent (represented as decimal)
Solving an Applied Problem Step 1. Read the problem, several times if necessary, until you understand what is given and what is to be found. Step 2. Assign a variable to represent the unknown value, using diagrams or tables as needed. Write down what the variable represents. Express any other unknown values in terms of the variable. Step 3. Write an equation using the variable expression(s). Step 4. Solve the equation. Step 5. State the answer to the problem. Does it seem reasonable? Step 6. Check the answer in the words of the original problem.
KEY TERMS FOR CHAPTER 2! linear equation in one variable solution solution set equivalent equations conditional equation contradiction identity mathematical model formula percent
2.1: Linear Equations in One Variable
ReplyDeleteLinear Equation in One Variable
A linear equation in one variable can be written in the form
Ax+B=C
where a,b, and c are real numbers, with a not equal to 0.
Addition and Multiplication Properties of Equality
ReplyDeleteAddition Property of Equality
For all real numbers, A,B, and C, the equations
A=B and A+C=B are equivalent.
In words, the same number may be added to each side of an equation without changing the solution set,
Multiplication Property of Equality
For all real numbers A and B, and for C not equal to 0, the equations
A=B and AC=BC are equivalent.
In words, each side of an equation may be multiplied by the same nonzero number without changing the solution set.
Solving a Linear Equation in One Variable
ReplyDeleteStep 1. Clear Fractions. Eliminate any fractions by multiplying each side by at the least common denominator.
Step 2. Simplify each side separately. Use the distributive property to clear parentheses and combine like terms as needed.
Step 3. Isolate the variable terms on one side. Use the addition property to get all terms with variables on one side of the equation and all numbers on the other.
Step 4. Isolate the variable. Use the multiplication property to get an equation with just the variable (with coefficient 1) on one side.
Step 5. Check. Substitute the proposed solution into the original equation.
2.2: Formulas
ReplyDeleteSolving for a Specified Variable
Step 1. Transform so that all terms containing the specified variable are on one side of the equation and all terms without that variable are on the other side.
Step 2. If necessary, use the distributive property to combine the terms with the specified variable. The result should be the product of a sum or difference and the variable.
Step 3. Divide each side by the factor that is the coefficient of the specified variable.
Solving a Percent Problem
ReplyDeleteLet a represent a partial amount of b, the base, or whole amount. Then the following formula can be used in solving a percent problem.
amount/base = a/b = percent (represented as decimal)
2.3 Applications of Linear Equations
ReplyDeleteVerbal expressions of Addition
sum
more than
plus
added to
increased by
Verbal Expressions of Subtraction
ReplyDeleteless than
minus
decreased by
subtracted from
difference between
Verbal Expressions of Multiplication
ReplyDeletetimes
multiplied by
of
twice
product
Verbal Expressions of Division
ReplyDeletequotient
divided by
ratio
Solving an Applied Problem
ReplyDeleteStep 1. Read the problem, several times if necessary, until you understand what is given and what is to be found.
Step 2. Assign a variable to represent the unknown value, using diagrams or tables as needed. Write down what the variable represents. Express any other unknown values in terms of the variable.
Step 3. Write an equation using the variable expression(s).
Step 4. Solve the equation.
Step 5. State the answer to the problem. Does it seem reasonable?
Step 6. Check the answer in the words of the original problem.
KEY TERMS FOR CHAPTER 2!
ReplyDeletelinear
equation in one variable
solution
solution set
equivalent
equations
conditional
equation
contradiction
identity
mathematical model
formula
percent