Solve absolute value equations Section 6.5 #44 There is nothing strange in the circle being the origin of any and every marvel. Aristotle

Concept We know absolute value as the distance a number is from zero We know absolute value as the distance a number is from zero We have yet to use the arithmetic involved when solving for an interior variable We have yet to use the arithmetic involved when solving for an interior variable Today we’re going to talk about this concept on our path to further discussion of inequalities Today we’re going to talk about this concept on our path to further discussion of inequalities

Lets look and this Evaluate Evaluate

Absolute Value Absolute Value is the distance between a number and zero on a number line

Solving with Absolute value Let’s solve this Let’s solve this When working with absolute values, we always have to account for the negative values that satisfy the equation

Solving with Absolute value When we look at this process, we essentially solve the equation twice When we look at this process, we essentially solve the equation twice Once with the positive value Once with the positive value Once with the negative value Once with the negative value

Solving with Absolute value Let’s solve this Let’s solve this

Bellwork Solution Solve for x Solve for x

Bellwork Solution Solve for x Solve for x

Solving Inequalities This process however is only valid with the absolute value is by itself This process however is only valid with the absolute value is by itself

Bellwork Solution Solve for x Solve for x

Bellwork Solution Solve for x Solve for x

Process Remove all the outside components until the absolute value is alone Split the equation into two: one with a positive the other negative Solve as usual Verify this answer makes sense ?

Solving Inequalities We have to pay attention to situations that don’t exist We have to pay attention to situations that don’t exist Absolute values can never be negative, so this situation yields no solution

Bellwork Solution Solve for x Solve for x

Bellwork Solution Solve for x Solve for x

Practical Example For this we use our understanding of absolute deviation which is given as Minimum=7.5 psi Maximum=8.5 psi Before the start of a professional basketball game, a basketball must be inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error of.5 psi (Absolute error is the absolute deviation of a measured value from an accepted value.) Find the minimum and maximum acceptable air pressures for the basketball.

Practical Example A volleyball league is preparing a two minute radio ad to announce tryouts. The ad has an absolute deviation of.05 minute. Find the minimum and maximum acceptable times the radio ad can be.

Most Important Points What’s the most important thing that we can learn from today? We can solve absolute value equalities by solving them twice, once for the positive value, once for the negative value Absolute deviation can be expressed as the absolute value of x minus the given value

Homework 6.5 1, 2-20 even, 21-32, 42-48