To solve the inequality [tex]\(-21 > 5u + 9\)[/tex] for [tex]\(u\)[/tex], follow these steps:
1. Isolate the term involving [tex]\(u\)[/tex]:
Start by moving the constant term (9) from the right-hand side to the left-hand side of the inequality:
[tex]\[
-21 - 9 > 5u
\][/tex]
2. Simplify the inequality:
Combine the constants on the left-hand side:
[tex]\[
-30 > 5u
\][/tex]
3. Solve for [tex]\(u\)[/tex]:
To isolate [tex]\(u\)[/tex], divide both sides of the inequality by 5 (the coefficient of [tex]\(u\)[/tex]):
[tex]\[
\frac{-30}{5} > u
\][/tex]
Simplify the division:
[tex]\[
-6 > u
\][/tex]
4. Rewrite the inequality:
It's common to write the variable on the left side for readability:
[tex]\[
u < -6
\][/tex]
Hence, the solution to the inequality [tex]\(-21 > 5u + 9\)[/tex] is:
[tex]\[
u < -6
\][/tex]
This means that [tex]\(u\)[/tex] must be less than [tex]\(-6\)[/tex].
