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 interpret the equation |x - a| = b?

Back

This equation means that the value x is within b units of a, which can be expressed as a - b ≤ x ≤ a + b.

Front

What does the expression |t - 425| = 15 represent in a real-world context?

Back

It represents a situation where the temperature t can vary 15 degrees above or below 425 degrees Fahrenheit.

Front

How can you rewrite the equation |x - 750| = 250 in interval notation?

Back

The interval notation for |x - 750| = 250 is [500, 1000].

Front

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

Back

'Plus or minus' indicates that the value can be either above or below a certain point, leading to two possible solutions.

Front

How do you solve the equation |x - 50| = 15?

Back

To solve |x - 50| = 15, you set up two equations: x - 50 = 15 and x - 50 = -15, leading to x = 65 and x = 35.

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 that point.

Front

In the context of the tennis racket problem, what does |x - 100| = 20 imply?

Back

It implies that the size of the racket head can vary from 80 square inches to 120 square inches.

Front

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

Back

You can determine the maximum and minimum values by solving the equation for both the positive and negative scenarios.

Front

What is the first step in solving an absolute value equation?

Back

The first step is to isolate the absolute value expression on one side of the equation.