Absolute Value Word Problems

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

How do you write an absolute value equation for a given value with a margin of error?

Back

If a value is 'a' with a margin of error 'b', the equation is written as |x - a| = b.

Front

What does the equation |v - 20| = 0.03 represent in a word problem?

Back

It represents that the volume 'v' of a liquid is within 0.03 ounces of 20 ounces.

Front

How do you determine the maximum and minimum values from an absolute value equation?

Back

To find the maximum and minimum values from |x - a| = b, solve for x: x = a + b and x = a - b.

Front

What is the significance of the 'plus or minus' in temperature-related problems?

Back

'Plus or minus' indicates a range of acceptable values around a target temperature.

Front

Write an absolute value equation for a goal of $75 with a variance of $6.50.

Back

|x - 75| = 6.50.

Front

What does the equation |x - 50| = 15 model in a real-life scenario?

Back

It models a situation where the actual amount of money is $50, with a possible variation of $15.

Front

How can absolute value equations be used in financial contexts?

Back

They can represent goals with acceptable variances, such as income or expenses.

Front

What is the general form of an absolute value equation?

Back

The general form is |x - a| = b, where 'a' is the center point and 'b' is the distance from 'a'.

Front

How do you interpret the solution of an absolute value equation?

Back

The solutions represent all possible values that satisfy the condition set by the equation.