Absolute Value Equations and Inequalities Assessment

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|.

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Back

x = 20 or x = -20.

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Back

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

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Back

x = -6 and x = 6.

Front

Back

x = 13 or x = -13.

Front

Explain the concept of absolute value inequalities.

Back

Absolute value inequalities express a range of values that a variable can take, based on its distance from a certain point.

Front

Back

x < -1 or x > 13.

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Back

It implies that x is within a distance of a from zero, resulting in the compound inequality -a < x < a.

Front

What is the graphical representation of an absolute value function?

Back

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.

Front

Back

Set up two equations: x + 3 = 5 and x + 3 = -5, then solve for x.