2-1 Solving 1 step equations Vocabulary: Equation - Addition property of equality Subtraction property of equality - solutions -isolate inverse operations - Multiplication property of equality Division property of equality - Equation: A mathematical sentence with an equal sign ex: X + 2 = 5 * an equation is like balancing a scale . If you do something to one side of the equation you must do something to the other side. ( You must keep the equation balanced ) ex: X + 2 = 5 * Come up with your own example and solve for it: Properties: Addition and subtraction properties of Equality 1.) If you add the same number to each side of an equation, the two sides remain equal. Arithmetic: 10=5(2), so 10 + 3 = 5(2) + 3 Algebra: If a=b, then a+c = b+c Come up with your own example of the property: 2.) If you subtract the same number from each side of an equation, the two sides remain equal. Arithmetic: 10= 5(2), so 10 - 3 = 5(2) - 3 Algebra: If a = b, then a - c = b - c

2-1 continued Write two problems of your own for addition and subtraction. (4 problems total) Solving Equations by multiplying and dividing Multiplication and division properties of equality 1) If each side of an equation is multiplied by the same number, the two sides remain equal. ex: Arithmetic Algebra 20= 40/2, so 2(20) =2(40/2) If a=b, then ac=bc 2.) If each side of an equation is divided by the same nonzero number, the two sides remain equal. 30= 3(10), so 30/6 = 3(10)/6 If a=b and c ≠ 0, then a/c = b/c * multiplication and division are inverse operations of each other and can be used to isolate and solve equations. Solving by mulitplying ex 3: solve X/ -7 = 15 Checking your work: Substitute your answer for your variable to check your work. both number on either side of your = should be =. a.

Solving by division ex 4: 816 = 8c 816= 8c 102= c try yourself: 3y= -12 Start homework: Sim so #29 Homework 2-1: 1-39 odd and 43- 49 odd page 65

2-1 notes continued a a solution to an equation is any value that makes the equation true. To find a solution: 1. isolate the variable or get the variable by alone on one side. use inverse Operations (opposite), operations that undo each other. Addition undoes subtraction and Subtraction undoes addition ex: 2 - 8 + 8 = 2 arithmetical 5 + 7 -7 = 5 n - 6 + 6 = n algebra n + 9 - 9 = n Write your own example of using inverse operations. ex for addition: -2 = k - 14 ex for subtraction: p + 35 = 243 isolate the variable Isolate the variable 1. P - 1 = -12 3. - 37 = y - 2 5. -36 = t - 14 7. a + 15 = 10