ALGEBRA
WORD PROBLEMS
1. Example #4:
Half a number plus 5 is 11. What is the number?
Solution
Let x be the number. Always replace "is" with an equal sign (1/2) x + 5 = 11
(1/2) x + 5 - 5 = 11 - 5
(1/2) x = 6
2 (1/2) x = 6 2
x = 12
2. Example #5:
The sum o
SOLUTIONS OF ALGEBRAIC
EQUATIONS
Up until now, we have just been talking about manipulating algebraic expressions. Now it is time
to talk about equations. An expression is just a statement like 2 x + 3. This expression might be
equal to any number, depend
Algebra
1. A volleyball court is shaped like a rectangle. It has a width of x meters and a length of 2x
meters. Which expression gives the area of the court in square meters?
A. 3x
B. 2 x 2
C. 3 x2
D. 2 x 3
Solution
l=2 x ; w=x
area=l w
2x x
The answer is
Algebra
1. Example #5:
The sum of two consecutive even integers is 26. What are the two numbers?
Solution
Let 2n be the first even integer and let 2n + 2 be the second integer
2n + 2n + 2 = 26
4n + 2 = 26
4n + 2 - 2 = 26 - 2
4n = 24
n=6
So the first even
Algebra
Like a Puzzle
In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can
(and cannot) do.
Here are some things we can do:
Clear out any fractions by Multiplying every term by the bottom parts.
Add or Subt
WORD PROBLEMS
Examples
Problems
WORD PROBLEMS require practice in translating verbal language into algebraic language. Se
Lesson 1, Problem 8. Yet, word problems fall into distinct types.
Below are some examples.
1. Example 1. ax b = c.
All problems like
Algebra
1. What is the equation of the line that has a slope of 4 and passes through the point (3, 10)?
Solution
The equation should be in the form y=mx +c
Where m is the slope of the line and c is the y intercept.
From the above equation; ymx=c
Given (3,
Algebra
1. What are the factors of x 211 x+ 24
Solution
We find two integers whose product is 24 while the sum is 11
The two integers are 83
Replacing the second term of the equation with the two integers we have
x 28 x3 x+24
Factorizing the equation, we
ADDITION PRINCIPLE
Equivalent Equations
The basic approach to finding the solution to equations are to change the equation into simpler
equations, but in such a way that the solution set of the new equation is the same as the solution
set of
the original
MULTIPLICATION PRINCIPLE
Multiplying (or dividing) the same non-zero number to both sides of an equation does not change
its solution set.
Example:
so if 6 x = 12, then 18 x = 36 for the same value of x (which in this case is x = 2).
The way we use the mu