Question

1. $-9 + 4r = 4r - 3 - 6$ 14) $4n + 5n + 15 = 5n + 7n$

Explanation:

Problem 12: $-9 + 4r = 4r - 3 - 6$

Step1: Simplify the right side

Simplify $-3 - 6$ on the right side.
$-3 - 6 = -9$, so the equation becomes $-9 + 4r = 4r - 9$.

Step2: Subtract $4r$ from both sides

Subtract $4r$ from each side of the equation:
$-9 + 4r - 4r = 4r - 9 - 4r$
Simplifying both sides gives $-9 = -9$.

Step1: Combine like terms

Combine the $n$ terms on both sides.
Left side: $4n + 5n = 9n$, so the left side becomes $9n + 15$.
Right side: $5n + 7n = 12n$, so the right side becomes $12n$.
The equation is now $9n + 15 = 12n$.

Step2: Subtract $9n$ from both sides

$9n + 15 - 9n = 12n - 9n$
Simplifying gives $15 = 3n$.

Step3: Divide both sides by 3

Divide each side by 3:
$\frac{15}{3} = \frac{3n}{3}$
Simplifying gives $5 = n$.

Answer:

This is an identity, so all real numbers are solutions.

Problem 14: $4n + 5n + 15 = 5n + 7n$