Answer/Discussion to 1a

The sum of a number and 2 is 6 less than twice that number.

Make sure that you read the question carefully several times. 

Since we are looking for a number, we will let 

*Inv. of add 2 is sub. 2
 

*Inv. of mult. by -1 is div. by -1

If you take the sum of 8 and 2 it is 6 less than twice 8, so this does check.
 

FINAL ANSWER: 

The number is 8.

(return to problem 1a)

Answer/Discussion to 1b

A rectangular garden has a width that is 8 feet less than twice the length.  Find the dimensions if the perimeter is 20 feet.

Make sure that you read the question carefully several times. 

We are looking for the length and width of the rectangle.  Since width can be written in terms of length, we will let

Width is 8 feet less than twice the length:

*Inv. of sub. 16 is add 16

*Inv. of mult. by 6 is div. by 6

If length is 6, then width, which is 8 feet less than twice the length, would have to be 4.  The perimeter of a rectangle with width of 4 feet and length of 6 feet is 20 feet.

FINAL ANSWER: 

(return to problem 1b)

Answer/Discussion to 1c

Complimentary angles, sum up to be 90 degrees.  Find the measure of each angle in the figure below.  Note that since the angles make up a right angle, they are complementary to each other.

Make sure that you read the question carefully several times. 

We are already given in the figure that

*Inv. of add 30 is sub. 30

*Inv. of mult. by 2 is div. by 2

If x is 30, then x + 30 = 60.  60 and 30 do add up to be 90, so they are complementary angles.

FINAL ANSWER:

(return to problem 1c)