Solving Inequalities and Absolute Value Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that shows the relationship between two expressions that are not equal, using symbols such as <, >, ≤, or ≥.

Front

What does |x| represent?

Back

|x| represents the absolute value of x, which is the distance of x from 0 on the number line, regardless of direction.

Front

How do you solve the inequality |x - a| < b?

Back

To solve |x - a| < b, split it into two inequalities: a - b < x < a + b.

Front

What does it mean if |x - a| > b?

Back

It means that x is either less than a - b or greater than a + b.

Front

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

Back

No Solution, because the absolute value cannot be negative.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, move all other terms to the other side of the equation.

Front

What is the solution to 2|5x - 1| + 3 = 9?

Back

x = 4/5 and x = -2/5.

Front

What type of inequality is |x - 2| < 7?

Back

AND compound inequality.

Front

How do you solve |2x - 3| = 5?

Back

Set up two equations: 2x - 3 = 5 and 2x - 3 = -5, leading to x = 4 and x = -1.

Front

What is the median of a set of numbers?

Back

The median is the middle value when the numbers are arranged in order.