E QUATIONS & I NEQUALITIES

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)

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 = 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 = 5(2) - 3if a = b, then a - c = b - c

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

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

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

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 – *the opposite of -14 is +14! -2 = 12 – 14 *what you do to one side you must do to the other = k -2 = -2 ✔ 12 = k

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

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.

H OMEWORK Textbook pg. 65 #1-14