Absolute Value Equations-Retake

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

How do you solve an absolute value equation of the form |x - a| = b?

Back

To solve |x - a| = b, set up two equations: x - a = b and x - a = -b. Solve each equation for x.

Front

What is the solution to the equation |x - 3| = 5?

Back

x = 8 or x = -2.

Front

What is the solution to the equation |5 - x| = 3?

Back

x = 2 or x = 8.

Front

What does it mean if |x| = 0?

Back

It means that x must be 0, as the only number with an absolute value of 0 is 0 itself.

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

How can you check your solution to an absolute value equation?

Back

Substitute your solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation |x + 4| = 6?

Back

x = 2 or x = -10.

Front

What is the solution to the equation |2x - 1| = 3?

Back

x = 2 or x = -1.

Front

What is the relationship between absolute value and distance?

Back

Absolute value represents the distance of a number from zero, and in equations, it can represent the distance between two points.