How many solutions does the equation have?

4(2n−4)+3=8n−19

Responses

0 solutions
0 solutions

1 solution
1 solution

infinitely many solutions

1 answer

Let's solve the equation step by step:

Given the equation:

\[ 4(2n - 4) + 3 = 8n - 19 \]

First, distribute the \(4\) on the left side:

\[ 4 \cdot 2n - 4 \cdot 4 + 3 = 8n - 19 \]

This simplifies to:

\[ 8n - 16 + 3 = 8n - 19 \]

Now combine the constants on the left side:

\[ 8n - 13 = 8n - 19 \]

Next, we'll isolate terms involving \(n\). We can subtract \(8n\) from both sides:

\[ -13 = -19 \]

This equation, \(-13 = -19\), is false.

Since we've arrived at a false statement, this means that there are no solutions to the original equation.

Thus, the answer is:

0 solutions