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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. ______________________