Solve each equation mentally.

x - 1 = 5

x = _____

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2(x - 1) = 10

x = _____

3(x - 1) = 15

x = _____

500 = 100(x - 1)

x = _____

Draw a tape diagram to represent each situation. For some of the situations, you need to decide what to represent with a variable.

Each of 5 gift bags contains x pencils. Tyler adds 3 more pencils to each bag. Altogether, the gift bags contain 20 pencils.

Draw your tape diagram on a piece of paper, take a picture of it, and upload the image using the image upload icon . Alternatively, You can make a tape diagram using the table button .

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Noah drew an equilateral triangle with sides of length 5 inches. He wants to increase the length of each side by x inches so the triangle is still equilateral and has a perimeter of 20 inches.

Draw your tape diagram on a piece of paper, take a picture of it, and upload the image using the image upload icon . Alternatively, You can make a tape diagram using the table button .

An art class charges each student $3 to attend plus a fee for supplies. Today, $20 was collected for the 5 students attending the class.

Draw your tape diagram on a piece of paper, take a picture of it, and upload the image using the image upload icon . Alternatively, You can make a tape diagram using the table button .

Elena ran 20 miles this week, which was three times as far as Clare ran this week. Clare ran 5 more miles this week than she did last week.

Match each situation to an equation. The situations are as follows:

1: Each of 5 gift bags contains x pencils. Tyler adds 3 more pencils to each bag. Altogether, the gift bags contain 20 pencils.

2: Noah drew an equilateral triangle with sides of length 5 inches. He wants to increase the length of each side by x inches so the triangle is still equilateral and has a perimeter of 20 inches.

3: An art class charges each student $3 to attend plus a fee for supplies. Today, $20 was collected for the 5 students attending the class.

4: Elena ran 20 miles this week, which was three times as far as Clare ran this week. Clare ran 5 more miles this week than she did last week.

Each situation in the previous activity is represented by one of the following equations.

(x + 3) * 5 = 20

3(x + 5) = 20

Check all the situations that match (x + 3) * 5 = 20, and leave all the situations that match 3(x + 5) = 20 unchecked.

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Find the solution to (x + 3) * 5 = 20. Use your diagrams to help you reason.

x = _____

Find the solution to 3(x + 5) = 20. Use your diagrams to help you reason.

x = ______

What does each solution tell you about its situation?

**Are you ready for more?**

Han, his sister, his dad, and his grandmother step onto a crowded bus with only 3 open seats for a 42-minute ride. They decide Han’s grandmother should sit for the entire ride. Han, his sister, and his dad take turns sitting in the remaining two seats, and Han’s dad sits 1.5 times as long as both Han and his sister. How many minutes did each one spend sitting?

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