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Q9.

Expert-verified
Found in: Page 80

### Pre-algebra

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$5a-\left(3a-7\right)\phantom{\rule{0ex}{0ex}}5a-3a-7\phantom{\rule{0ex}{0ex}}2a-7$

The correct expression is

$\begin{array}{c}5a-\left(3a-7\right)=5a-3a+7\\ =2a+7\end{array}$
See the step by step solution

## Step-1 – Apply the concept of terms and like terms

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:$a\left(b+c\right)=a\cdot b+a\cdot c$

## Step-2 – Use distributive property

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

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

## Step-3 – Group and combine like terms

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

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

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