Absolute Value Equations

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

How do you solve an absolute value equation of the form |x| = a?

Back

To solve |x| = a, set up two equations: x = a and x = -a.

Front

What is the solution to the equation |x - 5| = 3?

Back

x = 8 or x = 2.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given value (e.g., |x| = -1 has no solution).

Front

How do you isolate the absolute value in an equation?

Back

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

Front

What is the first step in solving the equation |2x + 1| = 7?

Back

Set up two equations: 2x + 1 = 7 and 2x + 1 = -7.

Front

What is the solution to the equation |x + 4| - 2 = 0?

Back

x = -2 or x = -6.

Front

How do you graph an absolute value function?

Back

An absolute value function forms a V shape on the graph, with the vertex at the point where the expression inside the absolute value equals zero.

Front

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

Back

x = 6 or x = 0.

Front

What is the relationship between absolute value and distance?

Back

Absolute value represents the distance of a number from zero, which can be thought of as the 'size' of the number without regard to its sign.