Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the equation |x| = a?

Back

Split the equation into two cases: x = a and x = -a, then solve for x.

Front

What does the equation |v + 8| - 5 = 2 represent?

Back

It represents the absolute value of (v + 8) being equal to 7, leading to two cases: v + 8 = 7 and v + 8 = -7.

Front

What is the first step in solving |x| = 16?

Back

Set up two separate equations: x = 16 and x = -16.

Front

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

Back

It means that there are no values of the variable that satisfy the equation, often due to a negative result inside the absolute value.

Front

How do you isolate the absolute value in an equation?

Back

Add or subtract terms from both sides of the equation until the absolute value expression is alone on one side.

Front

What is the solution to the equation |−4 + 5x| = 16?

Back

The solutions are x = 4/5 and x = -12/5.

Front

What is the significance of the negative sign in front of an absolute value?

Back

It indicates that the equation has no solution, as absolute values cannot be negative.

Front

How do you check your solutions for absolute value equations?

Back

Substitute the solutions back into the original equation to verify if both sides are equal.

Front

What is the general form of an absolute value equation?

Back

|ax + b| = c, where a, b, and c are constants.