To solve the equation [tex]\(-x + 7 = -4x - 11\)[/tex], follow these step-by-step instructions:
1. Start with Given Equation:
[tex]\[
-x + 7 = -4x - 11
\][/tex]
2. Isolate the Variable Term:
First, we want to get all the [tex]\(x\)[/tex] terms on one side of the equation and the constant terms on the other side. To do this, add [tex]\(4x\)[/tex] to both sides of the equation:
[tex]\[
-x + 4x + 7 = -4x + 4x - 11
\][/tex]
Simplifying both sides, we get:
[tex]\[
3x + 7 = -11
\][/tex]
3. Isolate the Constant Term:
Next, we want to isolate the [tex]\(3x\)[/tex] term by subtracting 7 from both sides of the equation:
[tex]\[
3x + 7 - 7 = -11 - 7
\][/tex]
Simplifying both sides, we get:
[tex]\[
3x = -18
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Finally, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 3:
[tex]\[
x = \frac{-18}{3}
\][/tex]
Simplifying gives:
[tex]\[
x = -6
\][/tex]
Therefore, the solution to the equation [tex]\(-x + 7 = -4x - 11\)[/tex] is:
[tex]\[
x = -6
\][/tex]
Among the given options, [tex]\(x = -6\)[/tex] is the correct answer.
