To solve the given equation [tex]\( 8q + 4p + 4 = 4q - 8 \)[/tex] for [tex]\( q \)[/tex], let's proceed with the following steps:
1. Start with the given equation:
[tex]\[ 8q + 4p + 4 = 4q - 8 \][/tex]
2. Move all terms involving [tex]\( q \)[/tex] to one side of the equation and the rest to the other side:
[tex]\[ 8q - 4q + 4p + 4 = -8 \][/tex]
Simplify:
[tex]\[ 4q + 4p + 4 = -8 \][/tex]
3. Isolate the term involving [tex]\( q \)[/tex]:
Subtract 4 from both sides:
[tex]\[ 4q + 4p = -8 - 4 \][/tex]
Simplify:
[tex]\[ 4q + 4p = -12 \][/tex]
4. Isolate [tex]\( q \)[/tex]:
Divide the entire equation by 4:
[tex]\[ q + p = -3 \][/tex]
5. Solve for [tex]\( q \)[/tex]:
[tex]\[ q = -p - 3 \][/tex]
Now, let's compare this solution with the proposed options:
1. [tex]\( q = -2p + 3 \)[/tex]
2. [tex]\( q = -p + 3 \)[/tex]
3. [tex]\( q = -p - 3 \)[/tex]
4. [tex]\( q = -2p - 3 \)[/tex]
By comparing, we see that the correct solution matches with:
[tex]\[ q = -p - 3 \][/tex]
Thus, [tex]\( q = -p - 3 \)[/tex] is the solution to the given equation.
