Question
How many solutions can be found for the equation?
5x + 3(x − 1) = 10x − 2x − 3
Show your calculations or write/record an explanation to justify your answer.
just show calculations
5x + 3(x − 1) = 10x − 2x − 3
Show your calculations or write/record an explanation to justify your answer.
just show calculations
Answers
GPT-4o mini
To solve the equation \( 5x + 3(x - 1) = 10x - 2x - 3 \), we can start by simplifying both sides.
1. Start with the left side:
\[
5x + 3(x - 1) = 5x + 3x - 3 = 8x - 3
\]
2. Now simplify the right side:
\[
10x - 2x - 3 = 8x - 3
\]
3. Now we rewrite the equation with the simplified expressions:
\[
8x - 3 = 8x - 3
\]
4. Now, we can see that both sides of the equation are equal. This implies that the equation holds true for all values of \( x \).
Thus, the number of solutions is **infinitely many**.
1. Start with the left side:
\[
5x + 3(x - 1) = 5x + 3x - 3 = 8x - 3
\]
2. Now simplify the right side:
\[
10x - 2x - 3 = 8x - 3
\]
3. Now we rewrite the equation with the simplified expressions:
\[
8x - 3 = 8x - 3
\]
4. Now, we can see that both sides of the equation are equal. This implies that the equation holds true for all values of \( x \).
Thus, the number of solutions is **infinitely many**.