Absolute Value Equations and Inequalities

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

What does the equation y = -|x| + 4 represent graphically?

Back

It represents a V-shaped graph that opens downwards, reflecting across the x-axis and shifted up 4 units.

Front

What is the solution set for the inequality |x - 3| < 5?

Back

The solution set is 3 - 5 < x < 3 + 5, which simplifies to -2 < x < 8.

Front

Can an absolute value equal a negative number?

Back

No, an absolute value cannot equal a negative number.

Front

What is the general form of an absolute value equation?

Back

The general form is |x - a| = b, where a is a constant and b is a non-negative number.

Front

How do you solve the equation |x + 4| = 7?

Back

Split into two cases: x + 4 = 7 and x + 4 = -7. Solutions are x = 3 and x = -11.

Front

What does the inequality |x + 2| > 5 mean?

Back

It means that x is either less than -3 or greater than 3.

Front

What is the solution to the equation |−2n| + 10 = −50?

Back

There is no solution because the left side cannot equal a negative number.

Front

How do you graph the inequality |x - 1| < 3?

Back

Graph the points x - 1 = 3 and x - 1 = -3, which gives the interval -2 < x < 4.

Front

What is the relationship between absolute value and distance?

Back

Absolute value represents the distance of a number from zero on the number line.