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Home > MC2 > Chapter 5 > Lesson 5.2.2 > Problem 5-56

5-56.
  1. Write the following expressions in two ways, one with parentheses and one without. For example, 4(x – 3) can be written 4x – 12. Homework Help ✎

    1. A number reduced by 3, then multiplied by 2.

    2. A number increased by 7, then multiplied by 5.

    3. Ten times a number, then add twenty.

Reducing by 3 means you first need to subtract 3 from a number. We will call this unknown number x. Then you will multiply that value by 2.

A number reduced by 3: (x − 3)

Then multiplied by 2: 2(x − 3)

Use the Distributive Property to multiply every term inside the parentheses by 2.

2x − 6

See part (a).

Ten times a number is 10x. Then add twenty to that to get: 10x + 20

Since 10 is a factor of both terms, we can factor out a 10 to get the following expression: 10(x + 2)

Check your answer by using the Distributive Property.