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Lesson 6.5 Solve Absolute Value Equations. Essential Question: How do you solve absolute value equations?. Before we start…. Why do and have the same solution?. What is absolute value ?. The distance a number is from zero on the number line. - PowerPoint PPT Presentation
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Lesson 6.5
Solve Absolute Value
Equations
Essential Question: How do you solve absolute value equations?
Before we start…
Why do and have the same solution?
What is absolute value?
The distance a number is from zero on the number line.
0 0
x x
x x
Solve 7x
Solve 3x
Solve 15x
How do you solve absolute value equations?
Given
Write two equations
and
Solve each equation.
Check each solution.
Solve 4 3x
Solve 5 7x
Solve 3 10x
Solve 5 10 45x
Solve 3 2 7 5 4x
Solve 3 4 2 7 11x
Can there be no solution?
• Yes there can be.
• The absolute value of a number is never negative so if the equation equals a negative number, there is no solution.
Solve 3 5 6 2x
What is absolute deviation?
• It is the absolute value of the difference of x and the given value.
• The absolute deviation can also be known as the absolute error if it’s a measured value from an accepted value.
Absolute Deviation given valuex
Basketballs 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 0.5 psi. Find the minimum and maximum acceptable air pressures for the basketball.
Guardrails A safety regulation requires that the height of a guardrail be 42 inches with an absolute deviation of 3 inches. Find the minimum and maximum heights of a guardrail.
Cheerleading A cheerleading team is preparing a dance program for a competition. The program must last 4 minutes with an absolute deviation of 5 seconds. Find the least and greatest possible times (in seconds) that the program can last.
Jewelry A jewelry store advertisement states that a certain diamond bracelet weighs 12 carats, but the actual weight can vary by as much as 5% of the advertised weight. Find the minimum and maximum possible weights of the bracelet.
• How do you solve absolute value equations?
Ticket Out the Door
Solve:
2 7 11d