Solving absolute value equations

Front

What is an absolute value equation?

Back

An absolute value equation is 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

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

Front

What is the absolute value of a negative number?

Back

The absolute value of a negative number is its positive counterpart. For example, |-5| = 5.

Front

What does the equation |x - 3| = 7 represent?

Back

It represents two scenarios: x - 3 = 7 and x - 3 = -7, leading to x = 10 and x = -4.

Front

How do you isolate the absolute value in an equation?

Back

To isolate the absolute value, you need to move all other terms to the opposite side of the equation.

Front

What is the first step in solving |2x + 1| = 5?

Back

The first step is to set up the two equations: 2x + 1 = 5 and 2x + 1 = -5.

Front

What is the solution to the equation |x + 4| = 0?

Back

The solution is x = -4, since the absolute value is zero only when the expression inside is zero.

Front

How do you check the solution of an absolute value equation?

Back

You substitute the solution back into the original equation to verify if both sides are equal.

Front

What is the absolute value of |-26|?

Back

The absolute value of |-26| is 26.

Front

What is the solution set for the equation |v + 8| - 5 = 2?

Back

The solution set is {-1, -15}.