# Beginning Algebra Tutorial 15

Beginning Algebra
Tutorial 15: Introduction to Problem Solving

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

x = a number

Step 3:  Carry out the plan (solve).

*Get all the x terms on one side

*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.

The number is 8.

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

L = length

Width is 8 feet less than twice the length:

2L - 8 = width

Step 3:  Carry out the plan (solve).

*Mult. (  ) by 2
*Combine like terms

*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.

Width is 4 feet.

Length is 6 feet.

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

x = 1 angle

x + 30 = other angle

Step 3:  Carry out the plan (solve).

*Combine like terms

*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.