Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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].