Download Integrated Algebra A and more Exercises Algebra in PDF only on Docsity!
Name______________________________ Date_______________
Integrated Algebra A
Notes/HW Packet 2
Lesson Homework
Translating Words into Algebraic Expressions HW Translating Words into Algebraic Equations HW Variables & Like Terms HW One-Step Equations (Add/Subt/Mult/Div) HW Solving Two-Step Equations HW Solving Multi-Step Equations with the Distributive Property HW
Solving Equations with Variable on Both Sides of Equal Sign HW
Solving Equations with Dist. Property & Variable on Both Sides
HW
Equation Review Completeworksheet
Review Sheet Test
Translating Words into Algebraic Expressions
We don’t only use the terms, add/subtract/multiply/divide when talking
about operations. Fill in the chart with other terms that can be used for
these operations.
Ways to write the operation
Emphasis on “less than”
Example: If I were to say, “How much is three less than five?” you are doing the math in your head. What you are doing in your head, even though it is an easy question, is “5 - 3.”
So when you see the words “less than” or a version of it, you must ___________ the terms and put a ____________________ sign in between them. (This also applies to terms with the word ‘from.’
Examples:
Five less than x. _______________________
Eight subtracted from g. _______________________
y less than fifteen. _______________________
Translating Words into Algebraic Equations
Expressions cannot be solved because they do not have an equal sign. Equations on the other hand have an equal sign! Yesterday, we learned how to translate words into algebraic expressions and today we are going to take that one step further!
Translate the following sentences into equations.
- Four times a number is 20. ________________________ *Can you figure out what “the number” is? ____
- A number decreased by 6 equals 8. ________________________ *Can you figure out what “the number” is? ____
- A number divided by 2 is 4. ________________________ *Can you figure out what “the number” is? ____
- 5 times a number, decreased by 7 is 13. ________________________
- When a number is subtracted ________________________ from 8, the result is 10.
- 9 less than twice a number is 10. ________________________
- The sum of 50 and a number is equal to ________________________ 6 times that number.
- 4 times a number increase by 5 exceeds ________________________ the number by 10.
Words that indicate when to put an “ = “ sign:
is equals
the result is exceeds by
Classwork:
A. Translate these expressions.
- Twice a number, increased by 8 ________________________
- 4 times the sum of a number and 7 ________________________
- 3 less than 6 times a number ________________________
- The sum of a number and 5, divided by 3 ________________________
B. Translate these equations.
- If two-thirds of a number is diminished ________________________ by 8, the result is 32.
- 10 times a number increased by 6 is 112. ________________________
- When a number is doubled, the result is 24. ________________________
- The product of a number and 11 is 99. ________________________
- 7 times the sum of a number and 4 ________________________ exceeds 3 times that number by 17.
Variables and Like Terms
Vocabulary
Variable - ___________________________________________________________
Coefficient - _________________________________________________________
Term - _______________________________________________________________
Like terms - ___________________________________________________________
Simplify - _____________________________________________________________
Number of terms: We count how many terms a polynomial has after combining all like terms. One term Two terms Three terms Four terms Ex: Ex: Ex: Ex:
We cannot count the number of terms unless all of the like terms have been put together so we must combine the like terms. When combining like terms you have to pay attention to the ______________________ attached and the _______________ in front of the coefficient.
Combining Like Terms Steps: Identify like terms. Combine the coefficients of the like terms and keep the common variable attached. Repeat this process for all sets of like terms. Separate all of your answers with addition/subtraction signs.
Examples:
5x + 3x ________________________________
5m^2 – 1m^2 + 8m – 3m^2 + 6m ________________________________
1xy + 3n – 2n + 4xy – 5 ________________________________
4a – 12b + 16 ________________________________
10x^2 + x – 7x^2 – x ________________________________
Practice
- 5x + 7x 2. -3x^2 + 10x^2 3. 13c – 12c
- 19y + y 5. 3yz – 5yz 6. – e + 8e
- 4a + 9 + a 8. 7s + 5x – 8s 9. 4.7x – 5.9x
- 5x – 6y – 8y + 7x 11. 23x + 8 + 6x + 3y 12. 4a^2 – 3 – 2a^2
- 10b^2 – 9b – 4b^2 + 6b 14. 5y^2 + y – 7y^2 - y
Solving One-Step Equations (+/-)
Now that we know how to set up equations , we are going to solve them using addition and/or subtraction!
Example 1 : x + 4 = 7
__________ [ Subtract 4 from each side to undo the addition]
[Here is your answer!]
Example 2: y – 3 = 12
__________ [ Add 3 to each side to undo the subtraction]
[Here is your answer!]
Our Goal : To isolate the variable (get the variable by itself on one side).
Solve the equation [Show ALL Work!] :
x = 4 – 7 2) x + 5 = 10 3) t – 2 = 6
11 = r – 4 5) -9 = 2 + y 6) n – 5 = -
-3 + x = 7 8) 5
= a - 5
- r – (-7) = 16
One-Step Equations ( (^) / (^) )
Today we are going to solve equations dealing with multiplications and division.
Example 1 : 6x = 18
[ Divide each side by 6 to undo the multiplication]
[Here is your answer!]
Example 2: 3
y = 9
[ Multiply both sides by -3 to undo the division]
[Here is your answer!]
Example 3: 5
^2 x = 4 [ Multiply both sides by the reciprocal to get rid of the fraction]
[Here is your answer!]
Solve the equation [Show ALL Work!] :
- 7x = 14 2) -6x = 24 3) 8
y = -
1 y = 10 5) - 81 = -9n 6) 3
^ x = -
- 12x = - 48 8) 4
^3 n = 12 9) -20x = -
Solving 2-Step Equations
☻ Solving equations is just a matter of undoing the operations that are being done to the variable. We already did 1-step equations… Example 1: Example 2:
x – 3 = -9 Operation Now: -5x = 30 Operation Now:
Opposite Operation: Opposite Operation:
Answer Answer
☻ In an equation which has more than one operation, we have to undo the operations in the correct order. First, undo addition or subtraction, then undo multiplication or division.
Example 1: 5x – 2 = 13 Let’s check our answer!
Example 2:^62 2
1 x Check
Example 3: 7 – x = -15 Check
Name________________________ Date____________________
“What do you call a crate of mallard ducks?”
- -7x – 7 = 49 5) 10 – 6x = 46 6) 9 = 6 – x
____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
- HW #
- 3x + 2 = 26 2) 4x – 5 = 35 3) 2x + 3 = Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke.
- 14x + 6 = 6 11) -1 – 8x = 7 12) 16 = -3x + 7) 2x – 1 = -9 8) -7 – 9x = -61 9) -23 = 7 – 15x
- I.
- A.
- B.
- K.
- N.
- E. -
- O. -
- Q. -
- Z.
- X.
- L. -
- S.
- R. -
- F. -
- M.
- D.
- C.
- D.
- C.
- W.
- U. -
Solving Multi-Step Equations with Distribution
Do you remember how to use the Distributive Property? Let’s see:
- 5(x + 2) 2) -2(6 – x)
Do you remember how to solve 2-step equations? I hope so! Let’s try:
- 5x – 2 = 18 2) 7 – x = -
Now, let’s put these two together and solve multi-step equations using the distributive property!
Example 1 : 5(x – 7) = 90
Example 2 : 3(x – 2) = 18
Example 3 :
1 (x + 6) = 12
IMPORTANT :
Leave the term with the variable ALONE until the last step!
Steps : Distribute the 5.
Add 35 to both sides.
Divide by 5 on both sides.
Check :
Check :
Check :
Name___________________________ Date____________________ HW #
“Who wrote the book ‘Grocery Packing at the Supermarket’?”
Solve for x. The answer to each problem will match a letter that will allow you to figure out the joke.
- 3(x + 2) = 21 2. 5(2x – 1) = -25 3. – 4(3x – 5) = -
- – 2(4 – x) – 5 = 11 5. 3(-6x + 7) + 4x = -7 6. 2(3x – 4) + 5(2x + 3) = -
- 5(x + 9) = 65 8. 2
(x – 3) = -4 9. 5x + 2(x – 6) + 7 = 2
- 9(x + 3) - 14x – 15 = 52
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
M. 7
R. 1
S. 3
Z. 9
E. -
A. -
U. 4
W. -
C. -
B. -
T. No Solution
D. -
F. 25
G. 12
L. 5
O. 6
S. 2
Solving Equations with Variable on Both Sides
Suppose there are variables on both sides of the equation. The trick now, is to get the variables on the same side by adding or subtracting them. Example 1:
4x + 5 = x – 4 We need to get the x over Check: with the 4x so we will subtract it from both sides.
Now we are at a 2-step equation! Let’s subtract 5 from both sides.
Divide by 3!
Example 2:
3x – 5 = 5x + 7 Check:
Example 3:
7y + 5 – 3y + 1 = 2y + 2 Check:
