when nicky tried to solve an equation using properties of equality, she ended up with the equation -3=-3. what equation mioght she have tried to solve? what is the solution of the equation?

-3 + 4*x^2 = - 3 + (2*x)^2

Any value of x is a solution for this eqution.

Step-by-step explanation:

She ended with -3 = -3

This is trivial, if we had an equation with one variable, something like:

f(x) = equation.

Ending with something like -3 = -3 means that we do not have any restriction with respect to x, so x could take any value.

This will happen if the terms with x in the left side are exactly the same as the terms in the right side, for exampe:

-3 + 4*x^2 = -3 + 4*x^2

In that case, we can substrrat 4*x^2 in both sides, and we will end with:

-3 = -3

This means that the solution for this equation is any value of x.

We also could rewrite this as:

-3 + 4*x^2 = - 3 + (2*x)^2

So the terms look different, but the terms are exactly the same for any value of x.

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.