Solve 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| = a where a > 0?

Back

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

Front

What is the solution to the equation |x| = 2.25?

Back

x = -2.25 or x = 2.25.

Front

How do you solve the equation |7x + 2| = 23?

Back

Set up two equations: 7x + 2 = 23 and 7x + 2 = -23. Solve each for x.

Front

What is the solution to the equation |4x + 1| = 15?

Back

x = 7/2 or x = -8.

Front

What is the solution to the equation |x + 1| = 8?

Back

x = 7 or x = -9.

Front

What is the solution to the equation |x| = 9?

Back

x = 9 or x = -9.

Front

What does it mean if an absolute value equation has no solution?

Back

It means that there are no values of x that can satisfy the equation.

Front

How do you graph an absolute value function?

Back

An absolute value function forms a V-shape on the graph, opening upwards if the coefficient of x is positive.

Front

What is the general form of an absolute value equation?

Back

The general form is |ax + b| = c, where a, b, and c are constants.