Question

match each equation to the number of solutions it has.
one solution no solution infinite number of solutions
$5x + 24 = 5(x + 5)$
$12p - 7 = -3p + 8$
$3x + 20 = 5x$

Explanation:

Step1: Simplify first equation

Start with $5x + 24 = 5(x + 5)$. Expand the right side:
$5x + 24 = 5x + 25$
Subtract $5x$ from both sides:
$24 = 25$
This is a false statement, so no solution.

Step2: Simplify second equation

Start with $12p - 7 = -3p + 8$. Add $3p$ to both sides:
$15p - 7 = 8$
Add 7 to both sides:
$15p = 15$
Divide by 15:
$p = 1$
This gives one unique solution.

Step3: Simplify third equation

Start with $3x + 20 = 5x$. Subtract $3x$ from both sides:
$20 = 2x$
Divide by 2:
$x = 10$
This gives one unique solution.

Answer:

• $5x + 24 = 5(x + 5)$: No solution
• $12p - 7 = -3p + 8$: One solution
• $3x + 20 = 5x$: One solution