Certainly! Let's solve the equation step-by-step:
Given equation:
[tex]\[
-8 - 3x = 19
\][/tex]
1. Isolate the term with the variable: We need to get the term involving [tex]\( x \)[/tex] by itself. We can start by eliminating the constant term on the left side.
- Add 8 to both sides of the equation to balance it.
[tex]\[
-8 - 3x + 8 = 19 + 8
\][/tex]
- Simplifying the left side, we get:
[tex]\[
-3x = 27
\][/tex]
2. Solve for [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], divide both sides of the equation by -3.
[tex]\[
x = \frac{27}{-3}
\][/tex]
- Simplifying the division, we obtain:
[tex]\[
x = -9
\][/tex]
Thus, the solution to the equation [tex]\( -8 - 3x = 19 \)[/tex] is:
[tex]\[
x = -9
\][/tex]
Check:
To verify our solution, substitute [tex]\( x = -9 \)[/tex] back into the original equation:
[tex]\[
-8 - 3(-9) = 19
\][/tex]
Simplify inside the parentheses and multiply:
[tex]\[
-8 + 27 = 19
\][/tex]
Adding the numbers together:
[tex]\[
19 = 19
\][/tex]
The left side equals the right side, confirming that our solution is correct.
So, [tex]\( x = -9 \)[/tex] is indeed the solution.
