Notes: Solving Equations
TLWBAT ____________ verbal _____________into __________ expressions and __________ and vice versa.
TLWBAT _______________ equations in ____________________ problems.
Vocabulary
Open Sentence __________________ containing one or more ______________
Equation a _______________sentence stating two mathematical ______________ are__________.
Solution when replacing the ________________ of an open sentence has a________ that makes the open
sentence______________.
Reflexive
Symmetric
a=a
a = b then b = a
Example:
Transitive
a= b, b = c, then a = c
Example:
Example:
Properties of Equality Examples:
Addition
Subtraction
Multiplication
Division
Basic Steps for Solving Equations:
1.
Identify the _________________.
2. ________________ both sides (distribute and/or combine like terms).
3. Move the ________________ to one side and the ________________ terms to the other side.
4. ____________________ by the number with the variable (in parentheses if it’s a fraction).
Example 1:
3(g + 7) = 2(2g + 1) – 5
Example 2:
A = 2L + 2W For W
Verbal Expressions and Equations: * Note See attached word sheet for verbal references.
Example 2
a) Twenty-five is five less than six n decreased by two
b) If the sum of six and a number is divided by two, the quotient is twelve.
Example 3:
1. Four times a certain number is the same as the number increased
by 78. Find the number.
1. _______________________
2. The sides of a triangle have lengths of y, 2y, and 3y – 6. What is
the length of each side if the perimeter is 60 inches?
2. _______________________
3. One angle of a triangle is twice as large as another. The third
angle is 20˚ more than the smallest angle. Find the measure of the
largest angle.
3. ______________________
Class/Homework
Name_______________
Algebra II/H
Date_______________
1. Five times the sum of a number and 12 is 32 less than four times
the number. What is the number?
1. _______________________
2. If 3 more than twice a number is decreased by 8 less than 4 times
the number, the result is the same as the original number decreased
by 16. What is the number?
2. _______________________
3. The sum of two numbers is 45. If 4 times the smaller is increased
by 3 times the larger, the result is 150. Find the numbers.
3. _______________________
4. One number is 12 less than three times another number. Their
sum is 188. What are the numbers?
4. _______________________
5. Three numbers have the sum of 107. The second number is 12
less than the first, and the third is 5 more than the second number.
Find the three numbers.
5. _______________________
6. A rectangular parking lot has a perimeter of 310 meters. The
length is 5 meters more than 4 times the width. What are the length
and the width?
6. length = ________
width = ________
7. Each of the legs of an isosceles triangle is 4 cm longer than the base. 7. _______________________
The perimeter of the triangle is 68 cm. Find the length of the base.
8. In the figure, a = x – 3, b = 2x – 12, and c = 3x + 15. Solve for x
and give the measure of each angle.
8. x = ______, a = ______
b = ______, c = ______
b˚
a˚
c˚
9. The two angles are supplementary. If a = 19x + 3 and
b = 21x + 17, solve for x and find the measure of each angle.
9. x = ________
a = ________
b = ________
a˚
b˚
10. The two angles are complementary if c = 2x – 25 and d = 3(x + 5),
solve for x and find the measure of each angle.
10. x = ________
c = ________
c˚
d = _______
d˚
11. The sides of a right triangle are a and b, and the hypotenuse is c.
Find a if b = 30 and c = 34.
11. ______________________
12. Find two numbers whose sum is 71 and whose difference is 21.
12. ______________________