Question

Describe and correct the error in simplifying

$$\begin{gathered} 5a-(3a-7) \\ 5a-3a-7 \\ 2a-7 \end{gathered}$$

Short answer

The correct expression is

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

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 constantterm 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:$a(b+c)=a\cdot b+a\cdot c$

Step-2 – Use distributive property

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

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

Step-3 – Group and combine like terms

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

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

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