Solving Absolute Value Equations and Word Problems

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

What does the equation |x| = a imply when a < 0?

Back

The equation |x| = a has no solution when a is less than 0, because absolute values cannot be negative.

Front

Solve for x: |x - 3| = 40

Back

x = 43 or x = -37.

Front

What is the solution set for the equation |n - 6| = -6?

Back

No solution, because absolute values cannot equal negative numbers.

Front

How do you find the solutions to |x - a| = b?

Back

You can find the solutions by setting up two equations: x - a = b and x - a = -b.

Front

What is the margin of error in a survey?

Back

The margin of error is a statistic that expresses the amount of random sampling error in a survey's results.

Front

If 89% of 400 adults pay their bills on time, how many adults is that?

Back

Approximately 356 adults (0.89 * 400).

Front

What is the interval of values for the percentage of adults who pay their bills on time with a 2% margin of error?

Back

The interval is 87% to 91%.

Front

How many solutions does the equation -4 = |-6v| - 4 have?

Back

One solution.

Front

What does the absolute value |x| represent?

Back

The absolute value |x| represents the distance of x from 0 on the number line.