Let's solve the equation [tex]\(0.2(x+1) + 0.5x = -0.3(x-4)\)[/tex] step by step.
1. Distribute the constants inside the parentheses:
[tex]\[
0.2(x + 1) + 0.5x = -0.3(x - 4)
\][/tex]
[tex]\[
0.2x + 0.2 + 0.5x = -0.3x + 1.2
\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[
0.2x + 0.5x + 0.2 = -0.3x + 1.2
\][/tex]
[tex]\[
0.7x + 0.2 = -0.3x + 1.2
\][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side and constants to the other side. Add [tex]\(0.3x\)[/tex] to both sides to eliminate [tex]\(-0.3x\)[/tex] from the right-hand side:
[tex]\[
0.7x + 0.3x + 0.2 = 1.2
\][/tex]
[tex]\[
1.0x + 0.2 = 1.2
\][/tex]
4. Subtract 0.2 from both sides to isolate [tex]\(x\)[/tex]:
[tex]\[
1.0x = 1.2 - 0.2
\][/tex]
[tex]\[
1.0x = 1.0
\][/tex]
5. Divide both sides by 1.0 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{1.0}{1.0}
\][/tex]
[tex]\[
x = 1
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(1\)[/tex].
The answer is [tex]\(\boxed{1}\)[/tex].
