Certainly! To solve the equation [tex]\(4m - 5(3m + 10) = 126\)[/tex], follow these steps:
1. Expand the term inside the parentheses:
Start by distributing the [tex]\(-5\)[/tex] across the terms inside the parentheses.
[tex]\[
4m - 5(3m + 10)
\][/tex]
Distribute [tex]\(-5\)[/tex]:
[tex]\[
4m - 5 \cdot 3m - 5 \cdot 10
\][/tex]
Simplifying each term:
[tex]\[
4m - 15m - 50
\][/tex]
2. Combine like terms:
Combine [tex]\(4m\)[/tex] and [tex]\(-15m\)[/tex]:
[tex]\[
4m - 15m = -11m
\][/tex]
Now, the equation looks like:
[tex]\[
-11m - 50 = 126
\][/tex]
3. Isolate the variable term:
Add 50 to both sides of the equation to move the constant term to the right side:
[tex]\[
-11m - 50 + 50 = 126 + 50
\][/tex]
Simplifying both sides:
[tex]\[
-11m = 176
\][/tex]
4. Solve for the variable:
Divide both sides by [tex]\(-11\)[/tex] to isolate [tex]\(m\)[/tex]:
[tex]\[
m = \frac{176}{-11}
\][/tex]
Simplifying the fraction:
[tex]\[
m = -16
\][/tex]
Thus, the solution to the equation [tex]\(4m - 5(3m + 10) = 126\)[/tex] is:
[tex]\[
m = -16
\][/tex]
