Certainly! To find the value of [tex]\(7x + 1\)[/tex] given the equation [tex]\(-2x - 1 = 7\)[/tex], we can follow these steps:
1. Solve for [tex]\(x\)[/tex] from the given equation:
The given equation is:
[tex]\[
-2x - 1 = 7
\][/tex]
To isolate [tex]\(x\)[/tex], first add 1 to both sides of the equation:
[tex]\[
-2x - 1 + 1 = 7 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
-2x = 8
\][/tex]
Next, divide both sides by -2 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{8}{-2}
\][/tex]
This simplifies to:
[tex]\[
x = -4
\][/tex]
2. Substitute the value of [tex]\(x\)[/tex] into [tex]\(7x + 1\)[/tex] to find its value:
Now that we have [tex]\(x = -4\)[/tex], we substitute this value into [tex]\(7x + 1\)[/tex]:
[tex]\[
7x + 1 = 7(-4) + 1
\][/tex]
Perform the multiplication:
[tex]\[
7(-4) = -28
\][/tex]
Now add 1:
[tex]\[
-28 + 1 = -27
\][/tex]
Therefore, the value of [tex]\(7x + 1\)[/tex] is [tex]\(-27\)[/tex].
So, to summarize:
- The solution for [tex]\(x\)[/tex] from the equation [tex]\(-2x - 1 = 7\)[/tex] is [tex]\(x = -4\)[/tex].
- Substituting [tex]\(x = -4\)[/tex] into [tex]\(7x + 1\)[/tex] results in [tex]\(7 \cdot (-4) + 1 = -27\)[/tex].
Hence, the value of [tex]\(7x + 1\)[/tex] is [tex]\(-27\)[/tex].
