Solving Equations as Formulas Algebra 1 ~ Chapter 3.8 Solving Equations as Formulas

Solving Formulas Some equations contain more than one variable. y = mx+b, P = a+b+c, A = ½bh At times, you will need to solve these equations for one of the variables. If the question asked you to solve for x, that would mean to get x by itself on one side of the equation, with no x’s on the other side. (x = __ ) Solve just like you did with equations that only had one variable (undo add/sub then mult/div)

How to Solve Formulas Example - Solve the equation A = ½bh, for h. Ask yourself: What is being done to h, the variable being solved for? (This is the same process as when we drove the car, and then we turned it around to go back home…) How do I undo what is being done? So: Just treat all other variables as if they were numbers, and repeat what we’ve already been doing.

A = ½bh, solve for h 2A = (½bh)2 2A = bh b b h = Solve for h means getting h = _________ Get rid of ½ by multiplying both sides by 2. Get h alone by “undoing” bh. Divide each side by b.

Example 1 t t Get r = ________ Solve d = r∙t, for r Undo multiplication Solve d = r∙t, for r d = r ∙ t t t

Example 2 Solve P = 2L + 2W, for L P – 2W = 2L 2 2 -2W -2W 2 2 Get “L” by itself, L=_______ Want to get rid of the whole term 2w, so subtract 2w from both sides of the equation. Undo 2L by dividing both sides by 2.

Example 3 Want to get x = __ “Undo” subtraction “Undo” multiplication Solve ax – c = b for x. +c +c ax = b + c a a Want to get x = __ “Undo” subtraction “Undo” multiplication

Example 4 Want to get y = __ Undo addition Undo multiplication Solve 6x – 3y = 12 for y. -6x -6x -3y = -6x + 12 -3 -3 y = 2x – 4 Want to get y = __ Undo addition Undo multiplication

Solve A = ½bh for b Solve 12x + 4y = 16 for y Solve V = lwh for h Lesson Quiz Solve A = ½bh for b Solve 12x + 4y = 16 for y Solve V = lwh for h