To solve the equation [tex]\( 8.6x - 3x + 4(x - 2) = -8 \)[/tex] and find the value of [tex]\( x \)[/tex] that makes it true, follow these steps:
1. Simplify the left-hand side of the equation:
Begin by combining like terms. The equation is currently:
[tex]\[
8.6x - 3x + 4(x - 2) = -8
\][/tex]
First, combine the terms that involve [tex]\( x \)[/tex]:
[tex]\[
(8.6 - 3 + 4)x + 4(-2) = -8
\][/tex]
2. Combine the coefficients of [tex]\( x \)[/tex]:
Calculate the coefficient sum:
[tex]\[
8.6 - 3 + 4 = 9.6 - 3 = 6.6
\][/tex]
So the equation simplifies to:
[tex]\[
6.6x + 4(-2) = -8
\][/tex]
3. Distribute and simplify the constant term:
Multiply [tex]\( 4 \)[/tex] by [tex]\( -2 \)[/tex]:
[tex]\[
6.6x - 8 = -8
\][/tex]
4. Isolate the variable term:
Add [tex]\( 8 \)[/tex] to both sides of the equation to isolate the [tex]\( x \)[/tex] term:
[tex]\[
6.6x = -8 + 8
\][/tex]
[tex]\[
6.6x = 0
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by [tex]\( 6.6 \)[/tex]:
[tex]\[
x = \frac{0}{6.6}
\][/tex]
[tex]\[
x = 0
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the equation [tex]\( 8.6x - 3x + 4(x - 2) = -8 \)[/tex] true is:
[tex]\[
x = 0
\][/tex]
