# 1. |-6 - 10| ? 2. (13 - 5(3 -7)^2)

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1. |-6 - 10|=?

The bars outside the problem are called absolute value bars. The absolute value stands for the distance, or number, from zero, which means that the answer is always positive. (-4 is four "spaces" from zero, just as +4 is four "spaces" from zero.)

In this case, you would solve: -6-10 = -16.

When you add in the absolute value bars, |-16| = 16, since you would have to move 16 "spaces" to get to zero.

2. (13 - 5(3 -7)^2)

When you see problems like this one, you'd usually want to start with the order of operations. The saying PEMDAS is useful, but sometimes people get confused with the MD and the AS, thinking that they have to work the problem in that exact order. I tell my students to think of it as PEMA: first parentheses, then exponents, and that you do either multiplication/division first and then addition/subtraction after.

You solve what's in the parenthesis first, but since it's all in parentheses, you start PEMA all over again -

(13 - 5(**3 -7**)^2)

(13 - 5(-4)^2)

Next comes exponents:

(13 - 5**(-4)^2**)

(13 - 5 (16))

Then multiplication/division:

(13 - **5 (16**))

(13 - 80)

Then addition/subtraction:

13-80 = -67

1) |-6 - 10| = ?

In this expression, the straight lines || mean "absolute value". The absolute value of a number is the distance from that number on the number line to 0. Thus, it is always positive.

To evaluate any expression containing absolute value, always calculate *whatever is inside the absolute value lines first. *In respect to the order of operations, absolute value is a grouping symbol, just like parenthesis.

Here, inside the absolute value lines is the expression -6 - 10 = -16.

-16 is the negative number, located 16 units to the left of 0 on the number line. The distance between -16 and 0 is 16 units.

|-16| = 16

**|-6 - 10| = 16**

2) 13 - 5(3 - 7)^2

To evaluate this expression, recall the order of operations agreement:

1) Parenthesis

2) Exponents

3) Multiplication/Division, from left to right

4) Addition/Subtraction, from left to right

Consider the expression above:

1) Parenthesis: (3 - 7) = -4

The expression is now 13 - 5(-4)^2

2) Exponent: (-4)^2 = (-4)(-4) = 16

The expression is now 13 - 5(16)

3) Multiplication: 5(16) = 80

4) Finally, subtraction: 13 - 80 = -67.

Thus, **13 - 5(3 - 7)^2 = -67**.

1. |-6 - 10|

Anything that happens to be inside absolute value will always be positive so |-a| will always equal a. So with this question you are going to add the contents inside together since they are both negative. Sometimes it helps for people to see the question asked as -6 + (-10) so the answer will be -16 which is inside absolute value so |-16|= 16

2. (13 - 5(3 -7)^2)

With this equation it's best to take it step by step.

(3 -7)^2 we are going to subtract the 3 from the -7

(-4)^2 then square it

(16) now put it back into the equation

13 - 5(16) Now multiply the 5(16)

13 -80 now subtract. You get...

-67 which is your answer!

**1. |-6-10|**

In order to solve this, we need to first solve the part within the lines (absolute value), than the lines are removed.

|-16|

**16**

**2. (13 - 5(3 -7)^2)**

The simple method of BODMAS (Brackets Of Division Multiplication Addition Subtraction) is to be applied to this.

(13-5(-4)^2)

(13-5(16))

(13-80)

**-67**

**1. |-6 - 10| ? **

|-16| = 16

**2. (13 - 5(3 -7)^2)**

** **(13-5(-4)^2)

(13-5(16))

(13-80)

(-67) = -67

2. (13 - 5(3 -7)^2)

**You use pemdas for a problem like this. Pemdas stands for **Parentheses,Exponents,(Multiplication,Division),(Addition,Subtraction)

Take care of the parentheses:

**5(3 - 7)^2**

**5(-4)^2**

**Exponent:**

**(13 -**5(16))

**Multiplication -5(16):**

**(13-80)**

**Subtraction:**

**-67 **

1. |-6 - 10|=?

For this problem, you would solve the inside like normal. The bars on the outside are called absolute value bars, which will make what ever answer you get a positive number.

-6-10=-16

|-16|=**16**

2. (13 - 5(3 -7)^2)

For this problem, you will use the rules of PEMDAS. Solve the parentheses first (the ones on the inside before the whole thing), then exponents, multiplication, etc.

(13-5(-4)^2)

(13-5(16))

(13-(80))

=**-67**