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 express a range of values using absolute value?

Back

A range of values can be expressed using absolute value as |x - a| = b, where 'a' is the central value and 'b' is the allowable deviation.

Front

What does the equation |x - 300| = 25 represent in a real-world context?

Back

It represents that the value 'x' can vary from 275 to 325, indicating a range of acceptable values around 300.

Front

How can you solve the equation |v + 8| = 7?

Back

To solve |v + 8| = 7, set up two equations: v + 8 = 7 and v + 8 = -7. Solving these gives v = -1 and v = -15.

Front

What is the significance of the 'plus or minus' in absolute value problems?

Back

'Plus or minus' indicates the range of acceptable values around a central point, showing how much variation is allowed.

Front

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

Back

The solution set of an absolute value equation represents all possible values that satisfy the condition defined by the equation.

Front

What is the general form of an absolute value equation?

Back

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

Front

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

Back

To find maximum and minimum values, solve the equation |x - a| = b to get x = a + b and x = a - b.

Front

What is an example of a real-world application of absolute value?

Back

An example is measuring temperature ranges, where the actual temperature can vary above or below a target temperature.

Front

How do you set up an absolute value equation from a word problem?

Back

Identify the central value and the allowable deviation, then express it in the form |x - central value| = deviation.