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Linear Equations in One Variable. Objective: To find solutions of linear equations. Linear Equations in One Variable. An equation in x is a statement that two algebraic expressions are equal. For example, 3x – 5 = 7 is an equation. Solutions of Equations.

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linear equations in one variable

Linear Equations in One Variable

Objective: To find solutions of linear equations.

linear equations in one variable1

Linear Equations in One Variable

An equation in x is a statement that two algebraic expressions are equal. For example, 3x – 5 = 7 is an equation.

solutions of equations
Solutions of Equations
  • To solve an equation in x means to find all values of x for which the equation is true. Such values are called solutions.
solutions of equations1
Solutions of Equations
  • To solve an equation in x means to find all values of x for which the equation is true. Such values are called solutions.
  • For instance, x = 4 is the solution of the equation 3x – 5 = 7 since replacing x with 4 makes a true statement.
identity vs conditional equation
Identity vs. Conditional Equation
  • Identity-An equation that is true for every real number in the domain of the variable.
identity vs conditional equation1
Identity vs. Conditional Equation
  • Identity-An equation that is true for every real number in the domain of the variable.
  • For example,

is an identity since it is always true.

identity vs conditional equation2
Identity vs. Conditional Equation
  • Conditional Equation-An equation that is true for just some (or even none) of the real numbers in the domain of the variable.
identity vs conditional equation3
Identity vs. Conditional Equation
  • Conditional Equation-An equation that is true for just some (or even none) of the real numbers in the domain of the variable.
  • For example,

is conditional because x = 3 and x = -3 are the only solutions.

definition of a linear equation
Definition of a Linear Equation
  • A linear equation in one variablex is an equation that can be written in the standard form ax + b = 0, where a and b are real numbers and a cannot equal 0.
example 1a
Example 1a
  • Solve the following linear equation.
example 1a1
Example 1a
  • Solve the following linear equation.
example 1b
Example 1b
  • You Try
  • Solve the following linear equation.
example 1b1
Example 1b
  • You Try
  • Solve the following linear equation.
example 2
Example 2
  • Solve the following linear equations.
example 21
Example 2
  • Solve the following linear equations.
example 22
Example 2
  • Solve the following linear equations.
linear equations in other forms
Linear Equations in other forms
  • Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator.
linear equations in other forms1
Linear Equations in other forms
  • Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator.
  • The common denominator is 12. Multiply everything by 12.
linear equations in other forms2
Linear Equations in other forms
  • Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator.
  • The common denominator is 12. Multiply everything by 12.
linear equations in other forms3
Linear Equations in other forms
  • You Try.
  • Solve the following equation.
linear equations in other forms4
Linear Equations in other forms
  • You Try.
  • Solve the following equation.
extra neous solutions
Extraneous Solutions
  • When multiplying or dividing an equation by a variable expression, it is possible to introduce an extraneous solution.
  • An extraneous solution is one that you get by solving the equation but does not satisfy the original equation.
example 4
Example 4
  • Solve the following.
example 41
Example 4
  • Solve the following.
example 42
Example 4
  • Solve the following.
example 43
Example 4
  • Solve the following.
example 44
Example 4
  • Solve the following.
  • If we try to replace each x value with x = -2, we will get a zero in the denominator of a fraction, which we cannot have. There are no solutions.
example 45
Example 4
  • You Try
  • Solve the following.
example 46
Example 4
  • You Try
  • Solve the following.
intercepts
Intercepts
  • To find the x-intercepts, set y equal to zero and solve for x.
intercepts1
Intercepts
  • To find the x-intercepts, set y equal to zero and solve for x.
  • To find the y-intercepts, set x equal to zero and solve for y.
intercepts2
Intercepts
  • To find the x-intercepts, set y equal to zero and solve for x.
  • To find the y-intercepts, set x equal to zero and solve for y.
  • Find the x and y-intercepts for the following equation.
intercepts3
Intercepts
  • To find the x-intercepts, set y equal to zero and solve for x.
  • To find the y-intercepts, set x equal to zero and solve for y.
  • Find the x and y-intercepts for the following equation.
  • x-intercept (y = 0)
intercepts4
Intercepts
  • To find the x-intercepts, set y equal to zero and solve for x.
  • To find the y-intercepts, set x equal to zero and solve for y.
  • Find the x and y-intercepts for the following equation.
  • x-intercept (y = 0)
  • y-intercept (x = 0)
intercepts5
Intercepts
  • You Try
  • Find the x and y-intercepts for the following equation.
intercepts6
Intercepts
  • You Try
  • Find the x and y-intercepts for the following equation.
  • x-intercept (y = 0)
  • y-intercept (x = 0)
class work
Class work
  • Pages 94-95
  • 23, 25, 29, 31, 34, 35, 46, 47
homework
Homework
  • Pages 94-95
  • 3-36, multiples of 3
  • 45-53 odd
  • 71,73,75
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