Question

How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
9x + 7x + 8 = −4 + 4(3x+5)

One solution

Infinitely many solutions

No solutions

Answer 1

To solve the equation \( 9x + 7x + 8 = -4 + 4(3x + 5) \), we can start simplifying both sides.

First, combine like terms on the left side:

\[
9x + 7x = 16x
\]
Thus, the left side becomes:

\[
16x + 8
\]

Next, let's simplify the right side of the equation:

\[
-4 + 4(3x + 5)
\]
Distributing the \(4\) gives:

\[
4 \cdot 3x + 4 \cdot 5 = 12x + 20
\]
So the right side simplifies to:

\[
-4 + 12x + 20 = 12x + 16
\]

Now we can rewrite the equation as:

\[
16x + 8 = 12x + 16
\]

Next, we will isolate \(x\). Subtract \(12x\) from both sides:

\[
16x - 12x + 8 = 16
\]
This simplifies to:

\[
4x + 8 = 16
\]

Next, subtract \(8\) from both sides:

\[
4x = 16 - 8
\]
Which simplifies to:

\[
4x = 8
\]

Now, divide both sides by \(4\):

\[
x = 2
\]

This gives us one solution: \(x = 2\).

Since there is only one solution, we conclude:

**One solution**.