Certainly! Let's simplify the expression step-by-step.
You have the expression:
[tex]\[ 9u + 4u - 5u - 2u + 4u \][/tex]
To simplify, we need to combine like terms. In this case, all terms involve [tex]\( u \)[/tex], so we will add and subtract the coefficients of [tex]\( u \)[/tex].
1. Identify the coefficients of [tex]\( u \)[/tex] in each term:
- The coefficient of [tex]\( u \)[/tex] in [tex]\( 9u \)[/tex] is [tex]\( 9 \)[/tex].
- The coefficient of [tex]\( u \)[/tex] in [tex]\( 4u \)[/tex] is [tex]\( 4 \)[/tex].
- The coefficient of [tex]\( u \)[/tex] in [tex]\( -5u \)[/tex] is [tex]\( -5 \)[/tex].
- The coefficient of [tex]\( u \)[/tex] in [tex]\( -2u \)[/tex] is [tex]\( -2 \)[/tex].
- The coefficient of [tex]\( u \)[/tex] in [tex]\( 4u \)[/tex] is [tex]\( 4 \)[/tex].
2. Add the coefficients together:
[tex]\[
9 + 4 - 5 - 2 + 4
\][/tex]
3. Perform the arithmetic step-by-step:
[tex]\[
(9 + 4) = 13
\][/tex]
[tex]\[
(13 - 5) = 8
\][/tex]
[tex]\[
(8 - 2) = 6
\][/tex]
[tex]\[
(6 + 4) = 10
\][/tex]
So, the sum of the coefficients is [tex]\( 10 \)[/tex].
4. Multiply the sum of the coefficients by [tex]\( u \)[/tex]:
[tex]\[
10u
\][/tex]
Therefore, the simplified expression is:
[tex]\[ \boxed{10u} \][/tex]
