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Chapter 2: Q. 12 (page 84)

Use the distributive property to write an equivalent variable expression.

鈥夆赌�49p+7

Short Answer

Expert verified

The equivalent variable expression is 36p+28.

Step by step solution

01

Step 1.  Distributive property

For any real numbers a, b, and c, the distributive property is given by:

ab+c=a鈰�b+a鈰�c

02

Step 2.  Example of distributive property

To evaluate the expression 34+t, distribute 3 to both the terms inside the parenthesis and remove the parenthesis sign to get

34+t=3鈰�4+3鈰�t=12+3t

03

Step 3.  Rewrite the given expression using distributive property

To write an equivalent variable expression for the given expression 49p+7, distribute 4 to both the terms inside the parenthesis and simplify further by multiplying the numbers as shown below

49p+7=4鈰�9p+4鈰�7=4鈰�9p+28=36p+28

Thus, the equivalent variable expression for the given expression is 36p+28.

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