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 by |x|.

Front

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

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

Solve the equation |2x + 9| = 15.

Back

x = 3 and x = -12.

Front

What is the solution to the equation |x - 3| = 0?

Back

x = 3.

Front

How do you solve an equation of the form |ax + b| = c?

Back

Isolate the absolute value, then set up two equations: ax + b = c and ax + b = -c.

Front

Solve the equation |2x - 3| + 5 = 10.

Back

x = -1 and x = 4.

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

Solve for a: |2a - 10| = 6.

Back

a = 8 and a = 2.

Front

What is the solution to the equation |5x| = 40?

Back

x = 8 and x = -8.

Front

How do you graph an absolute value function?

Back

The graph of an absolute value function forms a V shape, opening upwards, with the vertex at the point where the expression inside the absolute value equals zero.