Pd 2 Absolute value equation FLASHCARD

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, always expressed as a positive number.

Front

Solve the equation |x + 3| = 5. What are the two equations to solve?

Back

x + 3 = 5 and x + 3 = -5.

Front

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

Back

x = 2 and x = -1.

Front

Explain why absolute value is always positive.

Back

Absolute value represents distance from zero, and distance is always a non-negative quantity.

Front

What are the steps to solve an absolute value equation?

Back

1. Isolate the absolute value expression. 2. Set up two separate equations: one for the positive case and one for the negative case. 3. Solve both equations.

Front

Solve the equation |x - 4| + 2 = 6. What is the solution?

Back

x = 8 and x = 0.

Front

What does the equation |x| = a imply when a is positive?

Back

It implies that x = a or x = -a.

Front

Solve the equation |3x + 1| = 7. What are the solutions?

Back

x = 2 and x = -rac{8}{3}.

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.

Front

If |x| = 0, what is the value of x?

Back

x = 0.