Examples:

1. Combine like terms: [tex]5x + x - 7y[/tex]
[tex]\[
\begin{array}{ll}
5x + x - 7y & = \\
5x + 1x - 7y & = \\
(5 + 1)x - 7y & = 6x - 7y
\end{array}
\][/tex]
- Original problem
- When a coefficient is not visible, it is 1.
- Add coefficients of like terms ([tex]5x[/tex] and [tex]1x[/tex]); [tex] -7y[/tex] remains unchanged.

2. Combine like terms: [tex]12r + 5 + 3r - 5[/tex]
[tex]\[
\begin{array}{l}
12r + 5 + 3r - 5 \\
12r + 3r + 5 - 5 \\
(12 + 3)r + 5 - 5 \\
15r + 0 = 15r
\end{array}
\][/tex]
- Original problem
- Reorder terms
- Add coefficients of like terms ([tex]12r[/tex] and [tex]3r[/tex]); add constants ([tex]5[/tex] and [tex]-5[/tex])
- Simplify

---

1. Combine like terms:
[tex]\[
\begin{array}{l}
-2x + 11 + 6x - 2x + 6x + 11 \\
(-2 + 6)x + (-2 + 6)x + (11 + 11) \\
4x + 4x + 22 = 8x + 22
\end{array}
\][/tex]

2. Combine like terms:
[tex]\[
9a - 6a + 4b = (9 - 6)a + 4b = 3a + 4b
\][/tex]



Answer :

Sure, let's combine like terms in the expression [tex]\(9a - 6a + 4b\)[/tex]. Here is the detailed, step-by-step solution:

Step 1: Identify like terms.
- The terms [tex]\(9a\)[/tex] and [tex]\(6a\)[/tex] are like terms because they both have the variable [tex]\(a\)[/tex].
- The term [tex]\(4b\)[/tex] is different, as it has the variable [tex]\(b\)[/tex] and there are no other terms with [tex]\(b\)[/tex] to combine it with.

Step 2: Combine the coefficients of like terms.
- Combine the coefficients of [tex]\(a\)[/tex] from [tex]\(9a\)[/tex] and [tex]\(-6a\)[/tex].
[tex]\[ 9a - 6a = (9 - 6)a = 3a \][/tex]
- The term [tex]\(4b\)[/tex] remains as is because there are no other [tex]\(b\)[/tex] terms to combine with it.

Step 3: Write the simplified expression.
- After combining the coefficients of like terms, we get:
[tex]\[ 3a + 4b \][/tex]

Hence, the expression [tex]\(9a - 6a + 4b\)[/tex] simplifies to [tex]\(3a + 4b\)[/tex].