Solving 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

Solve for x: |x| = 5

Back

x = 5 or x = -5.

Front

What does it mean if |x - 3| = 0?

Back

It means that x is exactly 3, as the absolute value is zero only when the expression inside is zero.

Front

Solve for a: |2a - 10| = 6

Back

a = 8 or a = 2.

Front

What is the solution set for |x| = -3?

Back

No solution, as absolute values cannot be negative.

Front

Solve for n: |−2n| + 10 = −50

Back

No solution, as the left side cannot equal a negative number.

Front

What is the first step to solve |x + 4| = 7?

Back

Set up two equations: x + 4 = 7 and x + 4 = -7.

Front

Solve for v: |v + 8| − 5 = 2

Back

v = -1 or v = -15.

Front

What is the general form of an absolute value equation?

Back

|expression| = constant.

Front

If |x - 1| = 4, what are the possible values of x?

Back

x = 5 or x = -3.