To simplify the expression [tex]\(10x - 5y + 2x - 3y\)[/tex], follow these steps:
1. Identify and group like terms: The expression consists of terms involving [tex]\(x\)[/tex] and terms involving [tex]\(y\)[/tex].
- Terms involving [tex]\(x\)[/tex]: [tex]\(10x\)[/tex] and [tex]\(2x\)[/tex]
- Terms involving [tex]\(y\)[/tex]: [tex]\(-5y\)[/tex] and [tex]\(-3y\)[/tex]
2. Combine the coefficients:
- For the [tex]\(x\)[/tex] terms: Add the coefficients of [tex]\(10x\)[/tex] and [tex]\(2x\)[/tex]:
[tex]\[
10 + 2 = 12
\][/tex]
So, the combined [tex]\(x\)[/tex] term is [tex]\(12x\)[/tex].
- For the [tex]\(y\)[/tex] terms: Add the coefficients of [tex]\(-5y\)[/tex] and [tex]\(-3y\)[/tex]:
[tex]\[
-5 + (-3) = -8
\][/tex]
So, the combined [tex]\(y\)[/tex] term is [tex]\(-8y\)[/tex].
3. Form the simplified expression: Combine the results from step 2 to form the simplified expression:
[tex]\[
12x - 8y
\][/tex]
So, the simplified expression is:
[tex]\[
12x - 8y
\][/tex]
