In this video we will look at several examples of simplifying absolute value
expressions. Remember the absolute value of a number
is a numbers distance from zero. Because distance is always positive, the absolute
value of a number is always positive. We simplify absolute value expressions
following the order of operations shown below. And we treat absolute values just
as we treat grouping symbols or parentheses. For A, we have three times
the absolute value of negative six. The absolute value of negative six is
positive six. The expression simplifies to 3 times positive 6 which equals 18.
For B, we have four times the absolute value of negative 8 minus 6 times the
absolute value of 5 minus 1. Again treating the absolute values as grouping
symbols, the first step is to simplify inside the absolute value. Here, 5 minus 1
is 4. The expression simplifies to 4 times the absolute value of negative 8
minus 6 times absolute value of 4. Now we evaluate the absolute values. The
absolute value of negative 8 is positive 8. The absolute value of positive 4 is
positive 4. The expression simplifies to 4 times positive 8 minus 6 times
positive 4. Following the order of operations, we multiply before
subtracting. 4 times 8 is 32. 6 times 4 is 24,
giving us 32 minus 24 which equals 8.
For C, we have the absolute value of 9 minus 5 minus the absolute value of 7
minus 6. Again treating the absolute values as grouping symbols, we begin by
determining this difference and this difference inside the two absolute
values. 9 minus 5 is equal to 4. 7 minus 6 is equal to 1. The expression simplifies
to the absolute value of 4 minus the absolute value of 1. The absolute value
of positive 4 is positive 4. The absolute value of positive 1 is positive 1. The
expression simplifies to 4 minus 1 which equals 3. For D, we have 9 minus the
absolute value of 8 minus 4 times the quantity 7 minus 5. We begin by
simplifying inside the absolute value. Inside the absolute value we also have
parentheses, which means the first step is to determine 7-5. 7-5 equals 2. The
given expression simplifies to 9 minus the absolute value of 8 minus 4 times 2.
Still simplifying inside the absolute value, we multiply before subtracting. 4
times 2 is 8, giving us 9 minus the absolute value of 8 minus 8. 8 minus 8 is
0, giving us 9 minus the absolute value of 0. The absolute value of 0 is 0. 9 minus
0 is 9. The expression simplifies to positive 9. Let's look at one more
example. For E, we are given 3 plus the absolute value of 2 times the quantity 2
plus 3 minus 7. Once again we simplify inside the
absolute value first. Inside the absolute value we have additional parentheses. We
first determine the sum of 2 and 3. 2 plus 3 is 5. The expression simplifies to 3
plus the absolute value of 2 times 5 minus 7.
Still simplifying inside the absolute value, we multiply the before
subtracting. Two times five is ten, giving us three plus the absolute value of ten
minus seven. Finally inside the absolute value we have ten minus seven which is
three, giving us three plus the absolute value of three. The absolute value of 3
is 3. The expression simplifies to 3 plus 3 which is 6. I hope you found this
helpful.