To solve the equation [tex]\(2(t + 1) - 3 = -19\)[/tex], follow these detailed steps:
1. Distribute the 2 inside the parenthesis:
[tex]\[
2(t + 1) - 3 = 2t + 2 - 3
\][/tex]
2. Combine like terms:
[tex]\[
2t + 2 - 3 = 2t - 1
\][/tex]
3. Write the simplified equation:
[tex]\[
2t - 1 = -19
\][/tex]
4. Add 1 to both sides to isolate the term with the variable:
[tex]\[
2t - 1 + 1 = -19 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
2t = -18
\][/tex]
5. Divide both sides of the equation by 2 to solve for [tex]\(t\)[/tex]:
[tex]\[
\frac{2t}{2} = \frac{-18}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
t = -9
\][/tex]
So, the solution to the equation [tex]\(2(t + 1) - 3 = -19\)[/tex] is [tex]\(t = -9\)[/tex].
