Absolute Value Equations, Inequalities, and Transformations

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 the equation |v + 8| − 5 = 2.

Back

The solutions are v = -1 and v = -15.

Front

What does it mean if |x| = a, where a < 0?

Back

There is no solution, as absolute values cannot be negative.

Front

Solve the equation |6 - 2f| = -5.

Back

No solution, as absolute values cannot be negative.

Front

What is the solution set for |x + 3| ≤ 2?

Back

The solution is -5 ≤ x ≤ -1.

Front

What does the inequality |x + 1| ≥ 3 represent?

Back

It represents the values of x that are either less than or equal to -4 or greater than or equal to 2.

Front

If John is satisfied with a salary of $3000 with a tolerance of $500, what salaries would he accept?

Back

John would accept salaries between $2500 and $3500.

Front

What is the graphical representation of |x|?

Back

The graph of |x| is a V-shaped graph that opens upwards, intersecting the y-axis at (0,0).

Front

How do you solve an absolute value inequality?

Back

Split the inequality into two cases: one for the positive scenario and one for the negative scenario.

Front

What is the solution to the inequality |x - 4| < 3?

Back

The solution is 1 < x < 7.