Solving Absolute Value Equations

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 the equation |x - 3| = 4?

Back

Set up two equations: x - 3 = 4 and x - 3 = -4. Solve to find x = 7 and x = -1.

Front

What does the equation |x| = a imply when a > 0?

Back

It implies two solutions: x = a and x = -a.

Front

What is the absolute value of | -5 |?

Back

5

Front

How many solutions does the equation |x + 2| = 0 have?

Back

One solution: x = -2.

Front

What is the solution set for the equation |x| = 7?

Back

{7, -7}

Front

If |x| < 3, what is the range of x?

Back

-3 < x < 3.

Front

What is the solution to the equation |x - 1| = 5?

Back

x = 6 or x = -4.

Front

How do you interpret the expression |a| < |b|?

Back

It means the distance of a from zero is less than the distance of b from zero.

Front

What is the absolute value of |0|?

Back

0