Linear Equations in One Variable

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# Linear Equations in One Variable - PowerPoint PPT Presentation

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

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
• 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 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-An equation that is true for every real number in the domain of the variable.
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 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 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
• 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
• Solve the following linear equation.
Example 1a
• Solve the following linear equation.
Example 1b
• You Try
• Solve the following linear equation.
Example 1b
• You Try
• Solve the following linear equation.
Example 2
• Solve the following linear equations.
Example 2
• Solve the following linear equations.
Example 2
• Solve the following linear equations.
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 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 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 forms
• You Try.
• Solve the following equation.
Linear Equations in other forms
• You Try.
• Solve the following equation.
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
• Solve the following.
Example 4
• Solve the following.
Example 4
• Solve the following.
Example 4
• Solve the following.
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 4
• You Try
• Solve the following.
Example 4
• You Try
• Solve the following.
Intercepts
• To find the x-intercepts, set y equal to zero and solve for x.
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.
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.
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)
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)
Intercepts
• You Try
• Find the x and y-intercepts for the following equation.
Intercepts
• You Try
• Find the x and y-intercepts for the following equation.
• x-intercept (y = 0)
• y-intercept (x = 0)
Class work
• Pages 94-95
• 23, 25, 29, 31, 34, 35, 46, 47
Homework
• Pages 94-95
• 3-36, multiples of 3
• 45-53 odd
• 71,73,75