Solve for x : 5(x – 3) + 2 = 5(2x – 8) – 3
Answer : x = 6
Explanation:
The steps for solving this are as follows:
Apply the distributive property by multiplying the number outside of the parenthesis by each term inside the parenthesis to eliminate the parenthesis as follows:
5x – 15 + 2 = 10x – 40 – 3
Simplify both sides by adding or subtracting like terms as follows:
5x – 13 = 10x – 43
Eliminate 5x from the left side of the equation by adding a ( - 5x) to each side of the equation as follows:
5x + (-5x) – 13 = 10x + (-5x) – 43
-13 = 5x – 43
Add 43 to both sides as follows:
-13 + 43 = 5x – 43 + 43
30 = 5x
Multiply both sides by 1/5 as follows:
30 (1/5) = 5x (1/5)
6 = x
For additional information about the go to: Distributive property Page
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Friday, September 7, 2007
Thursday, September 6, 2007
Proportions - High School
While in Art class, Alex drew the door to his classroom to be 5 inches. The actual height of this door is 6 ft. 8 inches high. His teacher asked him to use this same scale factor to draw the classroom wall. If the actual height of the wall is 8 ft. how high should Alex draw the wall on his paper?
Answer: 6 inches
Explanation:
This is a proportion problem, however, in order to solve it we must first make sure that the measurements all use the same units. We notice that the problem uses units in inches and in feet. We must convert one into the other. Once the units match then the problem can be solved.
I have chosen to convert the feet into inches taking into consideration that there are 12 inches in one foot:
To convert the actual height of the door: [(6 ft) x (12 inches / 1 ft)] + 8 inches = 80 inches
Notice that the feet units cancel out and we are left with inches.
To convert the actual height of the wall: (8 ft) x (12 inches / 1 ft) = 96 inches
Notice that the feet units cancel out and we are left with inches.
Now we can set up the proportion:
Actual door height / drawn height = Actual wall height / X
80 inches / 5 inches = 96 inches / X
X = [(5 inches) (96 inches)] / 80 inches = 6 inches
Therefore, Alex should draw the wall 6 inches to have it proportional to the other measurements.
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Answer: 6 inches
Explanation:
This is a proportion problem, however, in order to solve it we must first make sure that the measurements all use the same units. We notice that the problem uses units in inches and in feet. We must convert one into the other. Once the units match then the problem can be solved.
I have chosen to convert the feet into inches taking into consideration that there are 12 inches in one foot:
To convert the actual height of the door: [(6 ft) x (12 inches / 1 ft)] + 8 inches = 80 inches
Notice that the feet units cancel out and we are left with inches.
To convert the actual height of the wall: (8 ft) x (12 inches / 1 ft) = 96 inches
Notice that the feet units cancel out and we are left with inches.
Now we can set up the proportion:
Actual door height / drawn height = Actual wall height / X
80 inches / 5 inches = 96 inches / X
X = [(5 inches) (96 inches)] / 80 inches = 6 inches
Therefore, Alex should draw the wall 6 inches to have it proportional to the other measurements.
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Wednesday, September 5, 2007
Area and Perimeter - Middle Grades
Find the area and the perimeter for the rectangle shown below when its width is 5 inches and its length is 14 inches:
Answer :
Area = 70 inches square
Perimeter = 38 inches
Explanation :
The formula to find the area of a rectangle is the width multiplied by the length. Therefore
A = (W) (L) = (5 in) (14 in) = 70 inches square
The formula to find the perimeter of a rectangle is twice the width added to twice the length. Therefore:
P = (2 W) + (2 L)
P = (2)(5 in) + (2)(14 in)
P = 10 in + 28 in = 38 inches
For additional information on this topic go to: Area and Perimeter
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Answer :Area = 70 inches square
Perimeter = 38 inches
Explanation :
The formula to find the area of a rectangle is the width multiplied by the length. Therefore
A = (W) (L) = (5 in) (14 in) = 70 inches square
The formula to find the perimeter of a rectangle is twice the width added to twice the length. Therefore:
P = (2 W) + (2 L)
P = (2)(5 in) + (2)(14 in)
P = 10 in + 28 in = 38 inches
For additional information on this topic go to: Area and Perimeter
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Tuesday, September 4, 2007
Addition and Subtraction - Elementary Math
On Monday Samantha bought 25 red shirts for school. On Tuesday, she went back to the store and bought an additional 15 red shirts. On Wednesday she washed 12 of them. How many more red shirts does she have to wash?
Answer : 28
Explanation:
This is an addition and subtraction problem. The goal is to find the number of red shirts that still have to be washed. In order to do that, first we must find the total number of shirts that she bought and then subtract the number of shirts that were washed. The final answer will give the number of shirts that are still left to be washed. Here goes:
Total number of shirts bought : 25 + 15 = 40 red shirts
Number of shirts left to be washed : 40 – 12 = 28 red shirts
For additional information on this subject go to the “ What is Addition and Subtraction” page.
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Answer : 28
Explanation:
This is an addition and subtraction problem. The goal is to find the number of red shirts that still have to be washed. In order to do that, first we must find the total number of shirts that she bought and then subtract the number of shirts that were washed. The final answer will give the number of shirts that are still left to be washed. Here goes:
Total number of shirts bought : 25 + 15 = 40 red shirts
Number of shirts left to be washed : 40 – 12 = 28 red shirts
For additional information on this subject go to the “ What is Addition and Subtraction” page.
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Monday, September 3, 2007
Greatest Common Factor (GCF) - College
Find the greatest common factor for the following polynomial:
Answer :
In order to solve the above, we must first define that the greatest common factor is the largest monomial that is a factor of each term of the polynomial. When we examine the numbers we find that the largest factor of each of the above numbers is 7. Now we must factor the variables. This is done by finding the variable with the highest exponent (power) that is a factor of :
This is found out to be:
Therefore b
y combining the two the answer will be:
© Copyright 2007.Najwa S. Hirn. All rights reserved.
Answer :
In order to solve the above, we must first define that the greatest common factor is the largest monomial that is a factor of each term of the polynomial. When we examine the numbers we find that the largest factor of each of the above numbers is 7. Now we must factor the variables. This is done by finding the variable with the highest exponent (power) that is a factor of :
This is found out to be:
Therefore b
y combining the two the answer will be:© Copyright 2007.Najwa S. Hirn. All rights reserved.
Sunday, September 2, 2007
Volume of a Cylinder - High School Math
Find the volume of the cylinder shown given that L = 30 inches and r = 3 inches Answer & Explanation:
A cylinder is a three dimensional geometric figure. The bases of the cylinder are two parallel and similar circles. The perpendicular line separating the two circles represents the height or length of the cylinder.
The formula for the volume of the cylinder is as follows where L is the height of the cylinder and r is the radius of the base of the cylinder :
With the given numbers and using 3.14 for pi the volume is calculated by multiplying the known values as follows:V = (3.14)(3 in x 3 in)(30 in) = 847.8 inches cubed
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Saturday, September 1, 2007
Number Line - Middle Level
What is the value of point B on the number line :
a. –6
b. 9
c. –12
d. 15
Answer : c
Explanation :
In Math, Integers are placed on a number line in marked, evenly spaced sections. A Zero divides this line into two segments. The positive integers appear on the right hand of the zero while the negative segments appear on the left hand of the zero. Each segment goes on to infinity therefore only the needed segment of the line is shown for each different math problem. The number line is a good tool to use when learning addition and subtraction of positive and negative integers. This will be covered in a different problem.
The above problem is a graphing problem showing the number line and requesting the identification of the value of a certain variable (in this case B) which is located on this line. A thorough examination of the line determines that the point B is located just above the integer
(-12). Therefore, the answer is ( c ) which is –12.
For a very detailed pictorial representation of the number line and additional description go to: Number line
©Copyright 2007.Najwa S. Hirn. All rights reserved.
Answer : c
Explanation :
In Math, Integers are placed on a number line in marked, evenly spaced sections. A Zero divides this line into two segments. The positive integers appear on the right hand of the zero while the negative segments appear on the left hand of the zero. Each segment goes on to infinity therefore only the needed segment of the line is shown for each different math problem. The number line is a good tool to use when learning addition and subtraction of positive and negative integers. This will be covered in a different problem.
The above problem is a graphing problem showing the number line and requesting the identification of the value of a certain variable (in this case B) which is located on this line. A thorough examination of the line determines that the point B is located just above the integer
(-12). Therefore, the answer is ( c ) which is –12.
For a very detailed pictorial representation of the number line and additional description go to: Number line
©Copyright 2007.Najwa S. Hirn. All rights reserved.
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