Algebra: Chapter 3-1 and 3-2, pages 114 and 119.
The Addition and Multiplication Properties of Equality (I call these 1 STEP EQUATIONS)
You can add, subtract, multiply or divide the same number to both sides of an equation and get an equivalent equation. We call these the addition and multiplication property of equality.
If `a=b`, then `a+c=b+c` and if `a=b`, then `ac=bc`
Subtraction and division are opposites of addition and multiplication, so we have no problems there. There are lots of examples at my favorite site, Purplemath, give these a look! Remember to show ALL the STEPS and that you can do these either vertically or horizontally. DON’T TAKE SHORTCUTS!
Examples:
(Addition)
`-6 = y-8`, we add 8, the opposite of -8
`-6+8=y-8+8`, we use the addition property to add 8 to both sides of the equation and finally,
`2=y`
(and Multiplication)
`y/9=14`, we will multiply both sides by `9/1` or just `9`
`9* (y/9)=9*14`, remembering that `9/9 =1`, we have
`y=126`
Whatever you do to an equation, do the S A M E thing to B O T H sides of that equation! If its `x+7`, then subtract 7 from both sides. If its `x-6`, then add 6 to both sides. If its `5x`, then divide both sides by `5` and if its `x/3`, then multiply both sides by `3`! Always do the opposite operation in these 1 step equations.