Question

9 sat in the given equation \\(3x + 9 = a(x + 3)\\), \\(a\\) is a constant. if the equation has infinitely many solutions, then the value of \\(a\\) is ______.

10 solve \\(ax - 2b = 5\\) for \\(x\\), where \\(a \
eq 0\\).

Explanation:

Expand the right side of Equation 9

Using the Distributive Property

$$ a(x + 3) = ax + 3a $$

Set up the identity for infinitely many solutions

Using the Number of Solutions concept

$$ 3x + 9 = ax + 3a $$

$$ a = 3 $$

Isolate the x term in Equation 10

Using the Solving Literal Equations concept

$$ ax - 2b = 5 $$

$$ ax = 5 + 2b $$

Solve for x

Using the Solving Literal Equations concept

$$ x = \frac{5 + 2b}{a} $$

Answer:

Question 9

The value of \(a\) is <blank>3</blank>.

Question 10

\(x = \frac{5 + 2b}{a}\)