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 solve an absolute value equation of the form |x - a| = b?

Back

To solve |x - a| = b, you set up two equations: x - a = b and x - a = -b, then solve for x.

Front

What does the equation |x - 4| = 5 represent?

Back

It represents two possible scenarios: x - 4 = 5 (x = 9) and x - 4 = -5 (x = -1).

Front

If |x - 3| = 7, what are the possible values of x?

Back

The possible values of x are 10 and -4.

Front

What is the general form of an absolute value inequality?

Back

An absolute value inequality can be expressed as |x - a| < b or |x - a| > b, representing a range of values.

Front

How do you graph an absolute value function?

Back

An absolute value function, y = |x|, forms a V-shape on the graph, with the vertex at the origin (0,0).

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, reflecting the two possible solutions in absolute value equations.

Front

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

Back

The solution set represents all possible values that satisfy the equation, often resulting in two distinct values.

Front

What is the equation for a temperature range of 425 degrees Fahrenheit, plus or minus 15 degrees?

Back

The equation is |t - 425| = 15.

Front

How do you write an equation for a price that varies around an average?

Back

If the average price is $750 and varies by $250, the equation is |x - 750| = 250.