Transcript Solving Equations

Writing and Simplifying
Algebraic
Expressions
Writing Phrases as an Algebraic Expression
An expression does not contain an equal sign and cannot be
solved, but it can be simplified.
An equation does contain an equal sign and can be solved.
Key Words
Added to, sum, increased, more than – means to add two things
together
Difference, subtracted from, minus – means to subtract
Multiply, product of – means to multiply
Quotient of, divided by – means to divide
Twice a number – means to multiply by 2
A number squared – means a number multiplied by itself twice (x2)
Let’s try some phrases…
The difference of a number and two, divided by five.
Let’s write our numbers and signs above the statement.
x
2
/
5
The difference of a number and two, divided by five.
When turning this phrase into an algebraic expression, we
have to ask ourselves “The difference of what?” It is the
difference between the x and 2 so it is written as x – 2.
( x  2) / 5
x2
5
Algebraically the second form is the correct form.
Next phrase…
Eight more than triple a number.
Let’s look at this phrase a different way.
8
+
3
x
Eight more than triple a number
The algebraic phrase would be 3x + 8. It is okay to write
the phrase as 8 + 3x but 3x + 8 would be the correct
algebraic form because we list our answers in order starting
with the variables followed by the constants.
And another one…
The sum of 3 times a number and 10, subtracted from 9 times a number.
Again, let’s write things out above the phrase:
+
3•x
10
9
The sum of 3 times a number and 10, subtracted from 9
•
x
times a number.
Again, ask yourself “The sum of what?” That is the sum of 3x + 10. The
subtracted from is very important here. Since it is stated this way, we are
subtracting the first part “from” the second part or
9x – (3x + 10).
Why did a put the 3x+10 in parentheses? Because the problem states to
subtract the “sum” of 3 times a number and 10. The minus sign outside
the parentheses will then be changed to addition and the sign of
everything inside will be changed to its opposite.
Combining Like Terms
• What is a term?
– A term can be any combination of a number
(coefficient), variable(s), and exponents.
Examples: 2, 3x, 4x2, or 5xy
• What are like terms?
– Like terms have the exact same variables and
exponents. Example: 3x and 7x both have the
same variable “x” so they are like terms.
Simplifying Algebraic Expressions
7x + 3x
They are like terms (both have an x variable) so we
simply add the coefficients together giving us
10x
10y2 + 2y2
Again, they are like terms (y2) because the
variables are the same. So we simply add the
coefficients together giving us
12y2
List the like terms in each set:
Set 1
5x
7y
7
6y
5x
4
12
3y
Set 2
4xy 9x
4x2y
4y
6
13yx
5yx2
17x
Set 3
9y2z 4yz
8zy2
8zy
9z
2yz
5yx2 5x
List the like terms in each set:
Set 1
5x
7y
7
6y
5x
4
12
3y
Answers: 5x and 5x; 7y, 6y, and 3y; 7, 4, and 12
Set 2
4xy 9x
4x2y 4y
6
13yx 5yx2 17x
Answers: 4xy and 13yx; 9x and 17x; 4x2y and 5yx2; 4y; 6
Set 3
9y2z 4yz
8zy2 8zy
9z
2yz
5yx2 5x
Answers: 9y2z and 8zy2; 4yz, 8zy, and 2yz; 9z; 5yx2 ; 5x
Combining Like Terms - Recap
• Like terms are a combination of
coefficients, variables, and exponents.
• The variables and exponents of each
number must match each other but they
can be in a different order.
• Once like terms are identified, you can
then proceed to add or subtract their
coefficients.
Adding and Subtracting Like Terms
1. 11b – 9a – 6b
2. 7x + 5y – 4x – 4y
3. 4a + 7b + 3 – 2a + 3b – 2
4. 2.3a + 7 + 4.7a + 3
5. 5m2 – 3m + 6m2
6. 5p2 + 2p + 8 + 4p2 + 5p – 6
7. Subtract 12a3 from 15a3
8. Subtract 8ab from the sum of 7ab and 5ab
9. 17r3s2-8r3s2
10. Subtract 4x2y from the sum of 6x2y and 12x2y
Do the work and then check your answers on the
next slide.
Answers to Adding and Subtracting
Like Terms
1. 5b – 9a
2. 3x + y
3. 2a + 10b +1
4. 7a + 10
5. 11m2 – 3m
6. 9p2 + 7p + 2
7. 3a3
8. 4ab
9. 9r3s2
10. 14x2y