Sure, let's solve the equation step by step:
Given the equation:
[tex]\[ 6c + 14 = -5c + 4 + 9c \][/tex]
First, combine the terms involving [tex]\(c\)[/tex] on the right side:
[tex]\[ -5c + 9c = 4c \][/tex]
So, the equation simplifies to:
[tex]\[ 6c + 14 = 4c + 4 \][/tex]
Next, to combine like terms involving [tex]\(c\)[/tex], subtract [tex]\(4c\)[/tex] from both sides:
[tex]\[ 6c - 4c + 14 = 4c - 4c + 4 \][/tex]
This simplifies to:
[tex]\[ 2c + 14 = 4 \][/tex]
To isolate the term with [tex]\(c\)[/tex], subtract 14 from both sides:
[tex]\[ 2c + 14 - 14 = 4 - 14 \][/tex]
[tex]\[ 2c = -10 \][/tex]
Finally, divide both sides by 2 to solve for [tex]\(c\)[/tex]:
[tex]\[ c = \frac{-10}{2} \][/tex]
[tex]\[ c = -5 \][/tex]
Therefore, the solution is:
[tex]\[ c = -5 \][/tex]
