Now that you’ve rewritten the left side of the equation without parentheses, take a look. How many solutions does this equation have? You may consider either using the structure of the equation or trying to isolate x on paper to help you figure out how many solutions this equation has.

Question

2(4x+5) = 10x+2
8x + 10 = 10x+2

Answer 1

To determine the number of solutions for the equation \(8x + 10 = 10x + 2\), we can first rewrite the equation in a simpler form.

Starting with:

\[ 8x + 10 = 10x + 2 \]

We can rearrange it by moving all terms containing \(x\) to one side and the constant terms to the other side:

1. Subtract \(8x\) from both sides:

\[ 10 = 2x + 2 \]

2. Next, subtract \(2\) from both sides:

\[ 8 = 2x \]

3. Finally, divide both sides by \(2\):

\[ x = 4 \]

Since we have isolated \(x\) and found a single value \(x = 4\), we conclude that the equation has one unique solution.