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 always non-negative.

Front

Solve for x: |x| = 7

Back

x = 7 or x = -7.

Front

What does the equation |a| = b imply when b < 0?

Back

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

Front

Solve for x: |2x - 3| = 5

Back

x = 4 or x = -1.

Front

What is the absolute value of |0|?

Back

0.

Front

Solve for x: |x + 4| = 10

Back

x = 6 or x = -14.

Front

What is the geometric interpretation of absolute value?

Back

It represents the distance from a point to the origin on a number line.

Front

Solve for k: |k - 9| = 4

Back

k = 5 or k = 13.

Front

If |x| = c, what are the possible values of x?

Back

x = c or x = -c.

Front

Solve for x: |3x + 2| = 5

Back

x = 1 or x = -2.333... .