To solve the equation [tex]\(5x + 8 - 3x = -10\)[/tex], follow these detailed steps:
1. Combine like terms: First, combine the terms involving [tex]\(x\)[/tex] on the left side of the equation. The terms [tex]\(5x\)[/tex] and [tex]\(-3x\)[/tex] can be combined.
[tex]\[
5x - 3x + 8 = -10
\][/tex]
2. Simplify: Simplify the equation by performing the subtraction in the combined terms.
[tex]\[
2x + 8 = -10
\][/tex]
3. Isolate the variable term: Next, we need to isolate the term containing [tex]\(x\)[/tex]. To do this, subtract 8 from both sides of the equation.
[tex]\[
2x + 8 - 8 = -10 - 8
\][/tex]
This simplifies to:
[tex]\[
2x = -18
\][/tex]
4. Solve for [tex]\(x\)[/tex]: Finally, solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 2.
[tex]\[
\frac{2x}{2} = \frac{-18}{2}
\][/tex]
This gives:
[tex]\[
x = -9
\][/tex]
Thus, the solution to the equation [tex]\(5x + 8 - 3x = -10\)[/tex] is [tex]\(\boxed{-9}\)[/tex].
