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Find the value of [tex]7x + 1[/tex] given that [tex]-2x - 1 = 7[/tex].

Simplify your answer as much as possible.


Sagot :

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].