Question 7284: State the property illustrated in each equation or statement.
1. (7 x s) x 7 x (s x t)
2. (6-2)a - 3b = 4a - 3b
Solve each equation.
3. 5r + 7 = 5r - 9
4. 5m - (5+4m) = (3 + m) - 8
Answer by glabow(165)   (Show Source):
You can put this solution on YOUR website! It's joke time in algebra -- well, not really. But these are "funny" problems.
The first looks like an example of how you can group numbers to do multiplication any way you want. That is, you can multiply a x b and then multiply by c [(a x b) x c] or you can multiply b x c and then multiply by a [a x (b x c)] and get the same answer. This is called the associative property.
The second equation shows that to multiply (6-2)a you get the same answer whether you do (4)a [subtracting in the group first] or 6a - 4a [multiplying each element of the group first and then doing the subtraction]. This shows that the sum of the products equals the product of the sums. And this is called the distributive property.
The third shows the equations of two lines. They have the same slope (5), but different y-intercepts (7 and -9). This means the lines are parallel and have no point in common. That is, there is no r that satisfies both equations. There is no solution.
The fourth shows the equation of a single line. Once you simplify the two sides you get m-5=m-5. Hmmmm... there is only one line. Any m you select is a "solution" of this equation. That is, any m satisfies both equations [which happen to be the same!]. So there are an uncountable number of solutions.
I don't know about you, but these strike me as "funny" answers!
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