Certainly! Let's break down the expression [tex]\(7t + 3b - 11x + 12y\)[/tex]. This expression contains four variables: [tex]\(t\)[/tex], [tex]\(b\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex]. Let's go through it step-by-step.
### Simplification of the Expression
1. Identify Variables and Coefficients
- [tex]\(t\)[/tex] is multiplied by 7, resulting in [tex]\(7t\)[/tex].
- [tex]\(b\)[/tex] is multiplied by 3, giving us [tex]\(3b\)[/tex].
- [tex]\(x\)[/tex] is multiplied by -11, giving us [tex]\(-11x\)[/tex].
- [tex]\(y\)[/tex] is multiplied by 12, yielding [tex]\(12y\)[/tex].
### Expression Form
So, the complete expression can be written as:
[tex]\[ 7t + 3b - 11x + 12y \][/tex]
### Evaluation of the Expression
In order to evaluate this expression, you would need to know the specific numerical values of the variables [tex]\(t\)[/tex], [tex]\(b\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex].
#### Example Evaluation
If you have specific values for each variable, say:
- [tex]\(t = 2\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(x = 1\)[/tex]
- [tex]\(y = 4\)[/tex]
You would substitute these values into the expression:
[tex]\[ 7(2) + 3(3) - 11(1) + 12(4) \][/tex]
And then perform the arithmetic operations:
1. [tex]\( 7 \times 2 = 14 \)[/tex]
2. [tex]\( 3 \times 3 = 9 \)[/tex]
3. [tex]\( -11 \times 1 = -11 \)[/tex]
4. [tex]\( 12 \times 4 = 48 \)[/tex]
Adding these results together:
[tex]\[ 14 + 9 - 11 + 48 = 60 \][/tex]
### Conclusion
Without specific values for [tex]\(t\)[/tex], [tex]\(b\)[/tex], [tex]\(x\)[/tex], and [tex]\(y\)[/tex], the expression cannot be numerically evaluated. Therefore, the final expression remains in the form:
[tex]\[ 7t + 3b - 11x + 12y \][/tex]
This is ready for evaluation if and when specific values for all the variables are provided.
