absolute value inequality

Front

What is the definition of absolute value?

Back

The absolute value of a number is the distance that number is from zero on the number line, regardless of direction.

Front

How do you solve the inequality |x + 3| < 8?

Back

To solve |x + 3| < 8, split it into two inequalities: -8 < x + 3 < 8. This simplifies to -11 < x < 5.

Front

What does the inequality |x - 6| < 4 represent in terms of 'and' or 'or'?

Back

The inequality |x - 6| < 4 represents an 'and' problem, meaning both conditions must be satisfied.

Front

How do you graph the solution to an absolute value inequality?

Back

To graph the solution, first solve the inequality, then plot the solution on a number line, using open circles for strict inequalities.

Front

What is the general form of an absolute value inequality?

Back

The general form of an absolute value inequality is |A| < B or |A| > B, where A is an expression and B is a non-negative number.

Front

What is the solution set for |x - 2| > 5?

Back

The solution set for |x - 2| > 5 is x < -3 or x > 7.

Front

How do you interpret the solution of an absolute value inequality?

Back

The solution of an absolute value inequality indicates the range of values that satisfy the condition, often expressed as intervals.

Front

What is the difference between |x| < a and |x| > a?

Back

|x| < a indicates values within a distance 'a' from zero, while |x| > a indicates values outside that distance.

Front

How do you solve |2x + 1| < 3?

Back

To solve |2x + 1| < 3, split into -3 < 2x + 1 < 3, leading to -2 < 2x < 2, and finally -1 < x < 1.

Front

What does the graph of |x| < 4 look like?

Back

The graph of |x| < 4 is a number line with open circles at -4 and 4, shading the region between them.