Certainly! Let's evaluate the expression step-by-step for [tex]\( a = 5 \)[/tex] and [tex]\( b = 1 \)[/tex]:
Given expression:
[tex]\[
12 + \left[ 2 - \left( 4 \cdot a^2 \right) \right] \div 7 + b
\][/tex]
1. Calculate [tex]\( 4 \cdot a^2 \)[/tex]:
[tex]\[
4 \cdot a^2 = 4 \cdot 5^2 = 4 \cdot 25 = 100
\][/tex]
Intermediate result:
[tex]\[
100
\][/tex]
2. Subtract this intermediate result from 2:
[tex]\[
2 - 100 = -98
\][/tex]
Intermediate result:
[tex]\[
-98
\][/tex]
3. Divide this by 7:
[tex]\[
-98 \div 7 = -14.0
\][/tex]
Intermediate result:
[tex]\[
-14.0
\][/tex]
4. Add 12 to the result:
[tex]\[
12 + (-14.0) = -2.0
\][/tex]
Intermediate result:
[tex]\[
-2.0
\][/tex]
5. Finally, add [tex]\( b \)[/tex] to the result:
[tex]\[
-2.0 + 1 = -1.0
\][/tex]
Final value:
[tex]\[
-1.0
\][/tex]
So, the value of the expression when [tex]\( a = 5 \)[/tex] and [tex]\( b = 1 \)[/tex] is [tex]\( -1.0 \)[/tex].
### Plotting on the Number Line
To plot [tex]\( -1.0 \)[/tex] on a number line, locate [tex]\( -1 \)[/tex] which is one unit to the left of zero. Mark this point clearly, indicating that it is the result of the given expression.
