Let's solve the equation step-by-step:
[tex]\[ 15x + (-x + 6) + (-5x + 4) = 7x + 23 - x + (3 - 2x) \][/tex]
First, simplify each side by combining like terms.
For the left-hand side:
[tex]\[ 15x + (-x + 6) + (-5x + 4) \][/tex]
Combine the terms involving [tex]\(x\)[/tex]:
[tex]\[ 15x - x - 5x = 9x \][/tex]
Combine the constant terms:
[tex]\[ 6 + 4 = 10 \][/tex]
So, the left-hand side simplifies to:
[tex]\[ 9x + 10 \][/tex]
Next, simplify the right-hand side:
[tex]\[ 7x + 23 - x + (3 - 2x) \][/tex]
Combine the terms involving [tex]\(x\)[/tex]:
[tex]\[ 7x - x - 2x = 4x \][/tex]
Combine the constant terms:
[tex]\[ 23 + 3 = 26 \][/tex]
So, the right-hand side simplifies to:
[tex]\[ 4x + 26 \][/tex]
Now, we have the simplified equation:
[tex]\[ 9x + 10 = 4x + 26 \][/tex]
Next, isolate the variable [tex]\(x\)[/tex]. Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[ 9x - 4x + 10 = 4x - 4x + 26 \][/tex]
This simplifies to:
[tex]\[ 5x + 10 = 26 \][/tex]
Subtract 10 from both sides to further isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 5x = 16 \][/tex]
Finally, divide both sides by 5:
[tex]\[ x = \frac{16}{5} \][/tex]
So, the solution to the equation is:
[tex]\[ x = \frac{16}{5} \][/tex]
