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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.

• To solve an equation in x means to find all values of x for which the equation is true. Such values are called solutions.

• 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-An equation that is true for every real number in the domain of the variable.

• 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.

• Conditional Equation-An equation that is true for just some (or even none) of the real numbers in the domain of the variable.

• 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.

• 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.

• Solve the following linear equation.

• Solve the following linear equation.

• You Try

• Solve the following linear equation.

• You Try

• Solve the following linear equation.

• Solve the following linear equations.

• Solve the following linear equations.

• Solve the following linear equations.

• Some equations involve fractions. Our goal is to get rid of the fraction by multiplying by the common denominator.

• 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.

• 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.

• You Try.

• Solve the following equation.

• 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.

• Solve the following.

• Solve the following.

• Solve the following.

• Solve the following.

• 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.

• You Try

• Solve the following.

• You Try

• Solve the following.

• To find the x-intercepts, set y equal to zero and solve for x.

• 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.

• 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.

• 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)

• 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)

• You Try

• Find the x and y-intercepts for the following equation.

• You Try

• Find the x and y-intercepts for the following equation.

• x-intercept (y = 0)

• y-intercept (x = 0)

• Pages 94-95

• 23, 25, 29, 31, 34, 35, 46, 47

• Pages 94-95

• 3-36, multiples of 3

• 45-53 odd

• 71,73,75