1 4 Solving Multistep Equations Variables on Both

1 -4 Solving Multistep Equations Variables on Both Sides Distribution Combining Like Terms

Definitions Coefficient – the number in front of the variable Constant – a term with no variable (just a plain number)

Step by Step Directions for Variable on Both Sides 1) Compare the coefficients of the variables 2) Solve for the variable on the side with the larger coefficient 3) Use the Golden Rule of Algebra to “move” the variables and constants to opposite sides 4) Check your solution!! – Still is and always will be the most important part of any solution

Example compare the coefficients of x 3 x + 5 = 4 x + 6 -3 x 5 = -6 x + 6 -6 -1 = x which is larger 3 or 4? solve for x on the right side, because 4 is bigger than 3 use Golden Rule of Algebra check your solution 3(-1) + 5 = 4(-1) + 6 -3 + 5 = 2 = -4 + 6 2 So x = -1 must be correct!!

Example 4 x + 10 = -2 x - 2 compare the coefficients of x which is larger? solve for x on the side with the largest coefficient of x use Golden Rule of Algebra check your solution

Example 3 d + 4 = 7 d - 12 compare the coefficients of d which is larger? solve for d on the side with the largest coefficient of d use Golden Rule of Algebra check your solution

Distribution 2 (x + 5) Think of the ( ) parentheses as a container (bag, suitcase, paper sack, halloween candy holder, etc. ) So inside this bag is an actual letter “x” and a five dollar bill. But the 2 in front means to multiply by 2. So we double the amount of bags we have. The contents of each bag remain the same.

Distribution 2(x + 5) So we get: 2 “x’s” and 2 five dollar bills 2(x + 5) = 2 ∙ x + 2∙ 5 = 2 x + 10

Example 3(c-4) = 15 3∙c - 3∙ 4 distribute 3 c – 12 = 15 use Golden Rule of Algebra +12 = +12 3 c = 27 3 3 c = 9 3(9 -4) = 15 3(5) = 15 check your solution So c = 9 must be correct!!

Example 2(9 x – 8) = 20 distribute use Golden Rule of Algebra check your solution

Example -4(6 + n) + 3 = 39 distribute use Golden Rule of Algebra check your solution

Does every equation have an answer? • If the variable drops out and what is left behind is true then the answer is: – Infinitely many solutions • If the variable drops out and what is left behind is false then the answer is: – No solution Algebra II

Step by Step Directions • • Distribution if needed Combine like terms Compare the coefficients of the variables Solve for the variable on the side with the larger coefficient • Use the Golden Rule of Algebra to “move” the variables and constants to opposite sides • Check your solution!! – Still is and always will be the most important part of any solution

Homework 1. 4 Worksheet