To solve the equation [tex]\(-12u - 9 + 7u = 26\)[/tex] for [tex]\(u\)[/tex], follow these detailed steps:
1. Combine like terms on the left side of the equation.
[tex]\[
-12u + 7u = -5u
\][/tex]
This simplifies the equation to:
[tex]\[
-5u - 9 = 26
\][/tex]
2. Add 9 to both sides of the equation to isolate the term with [tex]\(u\)[/tex] on the left side.
[tex]\[
-5u - 9 + 9 = 26 + 9
\][/tex]
Simplifying this, we get:
[tex]\[
-5u = 35
\][/tex]
3. Divide both sides of the equation by [tex]\(-5\)[/tex] to solve for [tex]\(u\)[/tex].
[tex]\[
u = \frac{35}{-5}
\][/tex]
Simplifying the division, we find:
[tex]\[
u = -7
\][/tex]
Thus, the solution to the equation [tex]\(-12u - 9 + 7u = 26\)[/tex] is:
[tex]\[
u = -7
\][/tex]
