Draw a rectangle to show that 5 (x + 2 ) and 5x + 10 are equivalent ?

First, we cannot draw a rectangle on these posts.

Second, 5 times x = 5x and 5 times 2 = 10.

Well, I could try to draw a rectangle to visually represent the equivalence between 5(x + 2) and 5x + 10, but I have a feeling it might end up looking more like a circus tent than an actual rectangle. So, let me humor you with a different approach!

Picture this: You have a group of 5 funny clowns eagerly waiting for their turn to perform. Now, clowns can be a bit unpredictable with their timing, so to ensure fairness, they decide to form a straight line outside the circus tent entrance. Let's say the distance between each clown is (x + 2) meters.

Now, if we want to calculate the total distance from the first clown to the last, we can multiply the distance between each clown, (x + 2), by the total number of clowns, which is 5. So we have 5(x + 2) meters of clown-waiting-line awesomeness!

But wait, there's more! As the clowns are waiting, some kind-hearted visitors hand each clown an extra 10 balloons, leading to extra cheer and hilarity. So now, each clown has 10 balloons, making a grand total of 5x + 10 balloons for the whole line of clowns.

So, even though it may not be a picture-perfect rectangle, you can see the equivalence between 5(x + 2) and 5x + 10 by imagining our fabulous line of clowns!

To show that 5(x + 2) and 5x + 10 are equivalent, we can draw a rectangle.

First, draw a rectangle and label one side as (x + 2).

Next, divide the rectangle into five equal parts vertically since the coefficient of the term (x + 2) is 5.

Label these five parts as 1(x + 2), 2(x + 2), 3(x + 2), 4(x + 2), and 5(x + 2).

Finally, write the expression 5x + 10 above the rectangle.

The rectangle will show that both expressions are equivalent since they represent the same area.

Here is the step-by-step process:

1. Draw a rectangle.
2. Label one side as (x + 2).
3. Divide the rectangle into five equal parts vertically.
4. Label these five parts as 1(x + 2), 2(x + 2), 3(x + 2), 4(x + 2), and 5(x + 2).
5. Write the expression 5x + 10 above the rectangle.

I hope this helps! Let me know if you have any further questions.

To visually show that 5(x + 2) and 5x + 10 are equivalent, we can draw a rectangle. Here's how to do it:

1. Start by drawing a rectangle and label the length of one of its sides as x + 2.

________________
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|__________________|

2. Next, divide the rectangle into five equal parts vertically, representing the coefficient 5.

_____ _____ _____ _____ _____
| | | | | |
| | | | | |
| | | | | |
|________|_______|______|______|____|

3. Label the top-left corner of each part with x.

_________ _________ ________ ________ ________
| x | x | x | x | x |
| | | | | |
| | | | | |
|________|_______|______|______|_____|

4. Finally, label the remaining top part as 2.

_________ _________ ________ ________ ________
| x | x | x | x | x |
| 2 | 2 | 2 | 2 | 2 |
| | | | | |
|________|_______|______|______|_____|

Now, you can see that the area of the rectangle is represented by 5(x + 2), where each part represents x + 2. Also, the expanded expression 5x + 10 shows that the 5 coefficient is multiplied by x, representing the length, and the 10 represents the sum of 2 added five times. Therefore, the rectangle visually demonstrates the equivalence between 5(x + 2) and 5x + 10.