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Linear Equations in One VariablePowerPoint Presentation

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.

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

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