To solve the equation [tex]\(-4x - 2 = x + 1\)[/tex], we need to isolate the variable [tex]\(x\)[/tex].
Let's go through the steps:
1. Move all terms involving [tex]\(x\)[/tex] to one side of the equation:
- Subtract [tex]\(x\)[/tex] from both sides to bring the [tex]\(x\)[/tex] terms together.
[tex]\[
-4x - x - 2 = 1
\][/tex]
2. Combine like terms:
- On the left-hand side, [tex]\(-4x - x\)[/tex] combines to [tex]\(-5x\)[/tex].
[tex]\[
-5x - 2 = 1
\][/tex]
3. Isolate the [tex]\(x\)[/tex] term:
- Add 2 to both sides of the equation to move the constant term.
[tex]\[
-5x = 1 + 2
\][/tex]
- Simplify the right side.
[tex]\[
-5x = 3
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
- Divide both sides of the equation by [tex]\(-5\)[/tex] to solve for [tex]\(x\)[/tex].
[tex]\[
x = \frac{3}{-5}
\][/tex]
- Simplify the fraction.
[tex]\[
x = -\frac{3}{5}
\][/tex]
- Convert the fraction to a decimal.
[tex]\[
x = -0.6
\][/tex]
Therefore, the solution to the equation [tex]\(-4x - 2 = x + 1\)[/tex] is [tex]\(x = -0.6\)[/tex].
