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Chapter 2: Q. 49 (page 80)

Use the distributive property to write an equivalent variable expression.

8(3t鈭�7)

Short Answer

Expert verified

The equivalent variable expression is24t鈭�56.

Step by step solution

01

. Distributive property

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

a(b+c)=a鈰�b+a鈰�c

02

. Example of distributive property

To evaluate the expression 3(4+t), distribute 3 to both the terms inside the parenthesis and remove the parenthesis sign to get

3(4+t)=3鈰�4+3鈰�t=12+3t

03

. Rewrite the given expression using distributive property

To write an equivalent variable expression for the given expression8(3t鈭�7), distribute 8 to both the terms inside the parenthesis and simplify further by multiplying the numbers as shown below

8(3t鈭�7)=8鈰�(3t)+8鈰�(鈭�7)=24t鈭�56.

Thus, the equivalent variable expression for the given expression is24t鈭�5624t鈭�56.

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