Certainly! Let's solve each of the equations step-by-step.
### 1. Solving [tex]$3 - t = -1$[/tex]
To isolate [tex]\( t \)[/tex], we can add [tex]\( t \)[/tex] to both sides and then add 1 to both sides:
[tex]\[ 3 - t = -1 \][/tex]
[tex]\[ 3 - (-1) = t \][/tex]
[tex]\[ t = 3 + 1 \][/tex]
[tex]\[ t = 4 \][/tex]
So the solution for the first equation is [tex]\( t = 4 \)[/tex].
### 2. Solving [tex]$2 \cdot 4 - 3p = -2$[/tex]
First, simplify the left-hand side:
[tex]\[ 2 \cdot 4 = 8 \][/tex]
So the equation becomes:
[tex]\[ 8 - 3p = -2 \][/tex]
Next, isolate [tex]\( p \)[/tex] by subtracting 8 from both sides:
[tex]\[ -3p = -2 - 8 \][/tex]
[tex]\[ -3p = -10 \][/tex]
Finally, divide both sides by -3:
[tex]\[ p = \frac{-10}{-3} \][/tex]
[tex]\[ p = \frac{10}{3} \approx 3.3333333333333335 \][/tex]
So the solution for the second equation is [tex]\( p \approx 3.3333333333333335 \)[/tex].
### 3. Solving [tex]$1 - 2t = 3$[/tex]
First, subtract 1 from both sides to isolate the term containing [tex]\( t \)[/tex]:
[tex]\[ 1 - 2t - 1 = 3 - 1 \][/tex]
[tex]\[ -2t = 2 \][/tex]
Next, divide both sides by -2:
[tex]\[ t = \frac{2}{-2} \][/tex]
[tex]\[ t = -1 \][/tex]
So the solution for the third equation is [tex]\( t = -1 \)[/tex].
### 4. Solving [tex]$4 \cdot 13 - a = 8$[/tex]
First, compute the left-hand side:
[tex]\[ 4 \cdot 13 = 52 \][/tex]
So the equation becomes:
[tex]\[ 52 - a = 8 \][/tex]
Next, isolate [tex]\( a \)[/tex] by subtracting 52 from both sides:
[tex]\[ -a = 8 - 52 \][/tex]
[tex]\[ -a = -44 \][/tex]
Finally, multiply both sides by -1:
[tex]\[ a = 44 \][/tex]
So the solution for the fourth equation is [tex]\( a = 44 \)[/tex].
In summary, the solutions are:
1. [tex]\( t = 4 \)[/tex]
2. [tex]\( p \approx 3.3333333333333335 \)[/tex]
3. [tex]\( t = -1 \)[/tex]
4. [tex]\( a = 44 \)[/tex]
