Solving Absolute value equations

Front

What is an absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative value.

Front

Solve for x: |x - 4| = 5

Back

x = 9 or x = -1

Front

What does the equation |a| = b imply?

Back

It implies that a = b or a = -b, where b is a non-negative number.

Front

Solve for x: 2|3x + 1| = 10

Back

x = 1 or x = -2

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.

Front

Solve for x: |2x - 3| = 7

Back

x = 5 or x = -2

Front

What is the significance of absolute value in real-world contexts?

Back

Absolute value is used to represent quantities that cannot be negative, such as distance, temperature differences, and financial losses.

Front

Solve for k: |k + 4| = 10

Back

k = 6 or k = -14

Front

What happens if the expression inside the absolute value is negative?

Back

The absolute value will convert it to a positive value, reflecting its distance from zero.

Front

Solve for x: |x + 2| = 0

Back

x = -2 (the only solution since absolute value cannot be negative).