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Q9.

Expert-verifiedFound in: Page 80

Book edition
Common Core Edition

Author(s)
Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages
183 pages

ISBN
9780547587776

**Describe and correct the error in simplifying**

The correct expression is

$\begin{array}{c}5a-(3a-7)=5a-3a+7\\ =2a+7\end{array}$In an algebraic expression, **terms** are separated by plus or minus signs.

The term **coefficient** refers to the number in front of the variable in any term of the expression.

A **constant **term is the number which have no variable associated with it.

**Like terms** are the terms which have identical variable parts with same exponent on it. Constants are considered to be like terms as well.

Distributive property:$a(b+c)=a\cdot b+a\cdot c$

To simplify the given expression $5a-(3a-7)$, first use the distributive property to remove the parenthesis as follows

$\begin{array}{c}5a-(3a-7)=5a-1\cdot \left(3a\right)-1\cdot (-7)\\ =5a-3a+7\end{array}$

Now to simplify above expression further, group the like terms and combine them as shown below

$\begin{array}{c}5a-(3a-7)=5a-1\cdot \left(3a\right)-1\cdot (-7)\\ =5a-3a+7\\ =(5-3)a+7\\ =\left(2\right)a+7\\ =2a+7\end{array}$

Thus, the simplified expression is $2a+7$

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