Certainly! Let's evaluate the expression [tex]\(6x - 2y + 5\)[/tex] given the values [tex]\(x = -2\)[/tex] and [tex]\(y = -7\)[/tex].
Here's a step-by-step solution:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
The expression is [tex]\(6x - 2y + 5\)[/tex]. We substitute [tex]\(x = -2\)[/tex] and [tex]\(y = -7\)[/tex]:
[tex]\[
6(-2) - 2(-7) + 5
\][/tex]
2. Multiply the constants by the substituted values:
- First, calculate [tex]\(6 \times (-2)\)[/tex]:
[tex]\[
6 \times (-2) = -12
\][/tex]
- Next, calculate [tex]\(-2 \times (-7)\)[/tex]:
[tex]\[
-2 \times (-7) = 14
\][/tex]
3. Substitute these results back into the expression:
Replacing the results we obtained, our expression now looks like this:
[tex]\[
-12 + 14 + 5
\][/tex]
4. Perform the addition and subtraction operations from left to right:
- First, add [tex]\(-12\)[/tex] and [tex]\(14\)[/tex]:
[tex]\[
-12 + 14 = 2
\][/tex]
- Next, add the result to [tex]\(5\)[/tex]:
[tex]\[
2 + 5 = 7
\][/tex]
Therefore, the value of the expression [tex]\(6x - 2y + 5\)[/tex] when [tex]\(x = -2\)[/tex] and [tex]\(y = -7\)[/tex] is:
[tex]\[
\boxed{7}
\][/tex]
