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 + 6| = 11?

Back

Set up two equations: x + 6 = 11 and x + 6 = -11. Solve to find x = 5 and x = -17.

Front

What does the equation |-4z| = 7 represent?

Back

It represents two cases: -4z = 7 and -4z = -7. Solving gives z = -7/4 and z = 7/4.

Front

How do you isolate the absolute value in the equation |t - 8| + 4 = 11?

Back

Subtract 4 from both sides to get |t - 8| = 7.

Front

What are the solutions to the equation |3x - 6| - 9 = -3?

Back

Add 9 to both sides to get |3x - 6| = 6. This leads to two equations: 3x - 6 = 6 and 3x - 6 = -6, giving x = 4 and x = 0.

Front

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

Back

It means that there are no values for the variable that can satisfy the equation, often because the absolute value cannot equal a negative number.

Front

How do you solve the equation |−2n| + 10 = −50?

Back

Subtract 10 from both sides to get |−2n| = -60. Since absolute values cannot be negative, this equation has no solution.

Front

What is the first step in solving an absolute value equation?

Back

Isolate the absolute value expression on one side of the equation.

Front

What are the two cases to consider when solving |x| = a?

Back

Case 1: x = a and Case 2: x = -a.

Front

How do you check your solutions for an absolute value equation?

Back

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