1. E QUATIONS & I NEQUALITIES

2. W ARM -U P Simplify each expression. 1.) 8 + (-1) 2.) 12 + (-12) 3.) -4 + (-7) 4.) 3 – 10 5.) -5 – 1 6.) 14 – (-12)

3. N OTES An equation is a mathematical sentence with an equal sign If you add the same number to each side of an equation, the two sides remain equal i.e. 10 = 5(2), so 10 + 3 = 5(2) + 3if a = b, then a + c = b + c If you subtract the same number from each side of an equation, the two sides remain equal. i.e. 10 = 5(2), so 10 - 3 = 5(2) - 3if a = b, then a - c = b - c

4. N OTES A solution to an equation is any value that makes the equation true To find a solution of an equation, isolate the variable, or get the variable alone on one side Inverse operations are operations that undo each other Use inverse operation to isolate a variable

5. R ULES /H INTS FOR SOLVING EQUATIONS Get the variable by itself. To get the variable by itself do the inverse operation (Two-Step Equations Only) Get rid of the number that is all alone first (same side as variable) For two-step equations repeat rules one and two(two- step equations require two-steps to get the solution For Check work “Plug it in, Plug it in”. If both sides are not equal on check work, then your answer is incorrect, try again

6. Y OUR “O PPOSITES ” OperationInverse Operation (“Opposites”) + Addition - Subtraction - Subtraction + Addition · Multiplication ÷ Division ÷ Division · Multiplication

7. E XAMPLE ( S ) Solve. 1.) -2 = k – 14 *k is the variable, he needs to be isolated Check Work -2 = k – 14 *to get k alone, -14 has to go! -2 = k – 14 + 14+ 14 *the opposite of -14 is +14! -2 = 12 – 14 *what you do to one side you must do to the other -2 + 14 = k -2 = -2 ✔ 12 = k

8. E XAMPLE ( S ) Solve each of the following. 2.) 17 = m + 213.) 31 = -15 + x 4.) x + (-13) = 215.) -14 + f = -21

9. E XAMPLE ( S ) 6.) Your aunt deposited $450 into her bank account. The new balance is $512. What was the original balance? Use an equation to solve.

10. H OMEWORK Textbook pg. 65 #1-14