absolute value/inequalities solving

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: |x + 4| < 5

Back

-9 < x < 1

Front

What does the inequality |4v + 12| ≥ 6 represent?

Back

It represents the values of v for which the expression 4v + 12 is either greater than or equal to 6 or less than or equal to -6.

Front

Solve: |4v + 12| ≥ 6

Back

v ≤ -4.5 or v ≥ -1.5

Front

Evaluate: |-12|

Back

12

Front

What is the solution set for |x + 3| > 8?

Back

x > 5 or x < -11

Front

Solve: 3|d - 4| ≥ 12

Back

d ≥ 8 or d ≤ 0

Front

What is the graphical representation of |x| < a?

Back

It represents the interval (-a, a) on the number line.

Front

What is the graphical representation of |x| ≥ a?

Back

It represents the union of the intervals (-∞, -a] and [a, ∞) on the number line.

Front

How do you isolate the variable in an absolute value equation?

Back

You split the equation into two cases: one for the positive scenario and one for the negative scenario.