Algebra: Chapter 3-1 and 3-2 (p 114 and 119)
The Addition and Muultiplication Properties of Equality
For all rational numbers, if `a=b`, then `a+c=b+c`
For all rational numbers, if `a=b`, then `ac=bc`
All that these things mean, is that you can add, subtract, multiply or divide BOTH sides of an EQUATION by the same number. The object of these 2 lessons is to SOLVE FOR X (the variable) by isolating it on ONE side of the equation and having all the numbers (NON-VARIABLES) on the other side.
Isolating the variable means keeping it BY ITSELF on one side.
For example, `y−4=-18`. To solve this equation, we ADD 4 to both sides
`y−4+4=−18+4`. We can combine like terms or constants. We know that `−18+4=−14` (the right side), and that `−4+4=0` (the left side), so we have
`y+0=−14` or `y=−14`, the solution.
For multiplying type problems, we do the same thing. For example:
`17c=459`. To isolate the c, we have to get rid of the 17 but it is multiplied by c. The opposite of multiplication is division, so we are going to DIVIDE both sides by `17`.
`17c/17=459/17` . We know that `17/17=1` and if we divide `459/17` we find the answer is `27`. So we have, by simplifiying the answer,
`c=27`
Things to remember for single step equations:
- If it is an addition problem, then subtract something from both sides to isolate the variable
- If it is a subtraction problem, then add something to both sides
- If it is a multiplication problem, then divide both sides by something
- If it is a division problem, then multiply both sides by something
In other words, DO THE OPPOSITE of what is next to the variable!
Here is a a link to Purplemath.com that has some great examples too.