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 denoted as |x|.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, set the expression inside the absolute value equal to both the positive and negative values of the other side of the equation.

Front

Solve for p: 9|9 - 2p| = 81

Back

p = 0, p = 9

Front

Solve for k: |6 - 2k| = 18

Back

k = -6, k = 12

Front

What does |x - a| = b represent?

Back

It represents two equations: x - a = b and x - a = -b.

Front

What is the solution to |x - 3| = 0?

Back

x = 3

Front

What does it mean if |x| = 0?

Back

It means x must be 0, as the only number with an absolute value of 0 is 0 itself.

Front

Solve for n: |−2n| + 10 = −50

Back

No Solution

Front

What is the graphical representation of an absolute value function?

Back

The graph of an absolute value function is a V-shape, opening upwards.

Front

What is the significance of the 'b' in |x - a| = b?

Back

The 'b' represents the distance from 'a' on the number line.