SOLVING EQUATIONS! {WITH DECIMALS}

U2L11

PS2 Solve single- and multi-step word problems involving operations with fractions and decimals and verify the solutions

DO NOW:JJ is baking a cake. He wants to double the recipe so he has enough to share with the whole class.The recipe calls for 3 ½ cups of flour. First he added 1 ¾ cup and later he added 2 ½ cups. How many more cups of flour does he need?

Planner:Hw p. 216 -217 #9, 22, 23, 38, 40, 41

WHAT IS AN EQUATION?

Equation: a mathematical statement that two things are equal. It consists of two expressions, one on each side

of an 'equals' sign. We know the left side and right side are equal

Equations are like a balance

scale

SOLVING AN EQUATION -- TERMINOLOGY

“Solving the equation” = The process of finding the value of the variables

We say "solve for x" - meaning solve the equation to find the value of the unknown number x that makes the statement true

In order to “solve for x”, we must “isolate the variable” (We need to get x alone on one side of the

equal sign) Goal is to end up with x = something

HOW TO SOLVE EQUATIONS To get x alone– UNDO every operation that is happening

to x UNDO perform the opposite operation Do PEMDAS in reverse! (add/subtract first, then multiply/divide,

etc)

Whatever you do to an equation,do the   S A M E   thingto   B O T H   sides of that equation! Keep the scale balanced

Example:x + 4.5 = 23.2 -4.5 -4.5 x = 18.7

•4.5 is being added to x, so we UNDO the operation by doing the opposite operation•Subtract 4.5 from BOTH SIDES•If I have x = something, I’m done

ANOTHER EXAMPLE

2x – 12.4 = 32.4 +12.4 +12.4

2x = 44.8 2 2 x = 22.4

•12.4 is being subtracted from x, so we UNDO it by ADDING 12.4 to both sides

•We don’t quite have x = something so we have more work to do

•X is being multiplied by 2, so we UNDO it by DIVIDING both sides by 2

•X = something, we are done!

I CAN SOLVE EQUATIONS…

"You gotta do the same thing on both sides“

Examples: p + 8 = 14.1 n + 4.7 = −4.7 x = −7 1.2 n + 3.9 = 0.7 −6.3n = −8.19 32.663 = p + 11.363

ASSIGNMENT

P. 216- 217 #9, 22, 23, 38, 40, 41