Question

evaluate the following.
(a) \\(\vert -3 \vert + 7 = \\)
(b) \\(\vert -3 + 7 \vert = \\)

Explanation:

Part (a)

Step1: Calculate the absolute value of -3

The absolute value of a number \( x \) is defined as \( |x|=

$$\begin{cases}x, & x\geq0\\ -x, & x < 0\end{cases}$$

\). For \( x=- 3\), since \(-3<0\), \(|-3|=-(-3) = 3\)

Step2: Add 7 to the result

Now we add 7 to the absolute value we just found. So \(|-3| + 7=3 + 7\)

Step3: Compute the sum

\(3+7 = 10\)

Step1: Simplify the expression inside the absolute value

First, we simplify \(-3 + 7\). \(-3+7=4\)

Step2: Calculate the absolute value of the result

Now we find the absolute value of 4. Since \(4\geq0\), \(|4| = 4\)

Answer:

\(10\)

Part (b)