Absolute Value Word Problems

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

The equation is written as |x - target| = range, where 'target' is the central value and 'range' is the allowable deviation.

It represents that the value x is 250 units away from 750, meaning x can be 1000 or 500.

To solve, set up two equations: v - 20 = 0.03 and v - 20 = -0.03. This gives v = 20.03 and v = 19.97.

The solution set is {35, 65}, meaning x can be 35 or 65.

It indicates that Victor's earnings are between $68.50 and $81.50.

It means x is either 10 - 5 = 5 or -10 - 5 = -15, so the solutions are x = 5 or x = -15.

The graph of an absolute value function is a V-shape, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.

The 'range' indicates how far the actual value can deviate from the target value.

You would use the equation |x - value| = 0, indicating that x must equal the value.