Linear equations in one variable
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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

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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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