Question

In the following exercise, simplify each expression.

(a)$-7+\left(-4\right)$

(b)$-7+4$

(c)$7+\left(-4\right)$

Short answer

Part (a) The simplified value is $-11$.

Part (b) The simplified value is $-3$.

Part (c) The simplified value is 3.

Step-by-step solution

Part (a) Step 1. Concept Used.

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (a) Step 2. Calculation.

Add $-4$to $-7$.

$\begin{array}{rcl}-7+\left(-4\right)& =& -7-4\\ & =& -11\end{array}$

Part (b) Step 1. Concept Used.

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (b) Step 2. Calculation. 

Add the opposite of 7 to 4 that is subtract 7 from 4.

$-7+4=-3$

Part (c) Step 1. Concept Used.

According to subtraction property, the subtraction of a number is equal to the addition of its opposite. This can be expressed as follows.

$a-b=a+\left(-b\right)$

Part (c) Step 2. Calculation.

Subtract 4 from 7.

$\begin{array}{rcl}7+\left(-4\right)& =& 7-4\\ & =& 3\end{array}$