Question

how many solutions does this equation have?
$15p - 12 = 9 + 19p - 1$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Simplify right-hand side

Combine constants: $9 - 1 = 8$, so equation becomes $15p - 12 = 19p + 8$

Step2: Isolate variable terms

Subtract $15p$ from both sides:
$15p - 15p - 12 = 19p - 15p + 8$
$-12 = 4p + 8$

Step3: Isolate constant terms

Subtract 8 from both sides:
$-12 - 8 = 4p + 8 - 8$
$-20 = 4p$

Step4: Solve for $p$

Divide both sides by 4:
$p = \frac{-20}{4} = -5$

Answer:

one solution