Certainly! Let's break down the given expression step-by-step:
Given:
[tex]\[ a = -3 \][/tex]
[tex]\[ b = -2 \][/tex]
We need to evaluate the expression:
[tex]\[ 4(2a - 1) + 3b + 11 \][/tex]
1. First, calculate the expression inside the parentheses:
[tex]\[ 2a - 1 \][/tex]
Substitute [tex]\( a = -3 \)[/tex]:
[tex]\[ 2(-3) - 1 = -6 - 1 = -7 \][/tex]
So the value of the expression [tex]\( 2a - 1 \)[/tex] is [tex]\(-7\)[/tex].
2. Next, multiply this result by 4:
[tex]\[ 4(-7) = -28 \][/tex]
3. Now, calculate the product of 3 and [tex]\( b \)[/tex]:
[tex]\[ 3b \][/tex]
Substitute [tex]\( b = -2 \)[/tex]:
[tex]\[ 3(-2) = -6 \][/tex]
4. Finally, add the results from steps 2 and 3 and also add 11:
[tex]\[ -28 + (-6) + 11 \][/tex]
Step-by-step addition:
[tex]\[ -28 + (-6) = -34 \][/tex]
[tex]\[ -34 + 11 = -23 \][/tex]
Thus, the final result of the expression [tex]\( 4(2a - 1) + 3b + 11 \)[/tex] is [tex]\(-23\)[/tex].
Hence, the complete step-by-step calculations yield:
- Intermediate result for [tex]\( 2a - 1 \)[/tex] is [tex]\( -7 \)[/tex].
- Multiplying by 4, the intermediate result is [tex]\( -28 \)[/tex].
- The value of [tex]\( 3b \)[/tex] is [tex]\( -6 \)[/tex].
- The final result after adding [tex]\(-28\)[/tex], [tex]\(-6\)[/tex], and 11 is [tex]\(-23\)[/tex].
