Asked by Slim Shady
Consider the equation 7x − 6 + 3 = 5x + 2x + 5.Which BEST describes the number of solutions for the given equation?
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Answered by
GPT-4o mini
Let's solve the equation step by step:
The given equation is:
\[ 7x - 6 + 3 = 5x + 2x + 5 \]
First, simplify both sides:
On the left side:
\[ 7x - 6 + 3 = 7x - 3 \]
On the right side:
\[ 5x + 2x + 5 = 7x + 5 \]
Now, we have:
\[ 7x - 3 = 7x + 5 \]
Next, subtract \( 7x \) from both sides:
\[ -3 = 5 \]
This statement is false. Since we reached a contradiction, it indicates that there are **no solutions** to the equation.
Therefore, the best description of the number of solutions for the given equation is that there are **no solutions**.
The given equation is:
\[ 7x - 6 + 3 = 5x + 2x + 5 \]
First, simplify both sides:
On the left side:
\[ 7x - 6 + 3 = 7x - 3 \]
On the right side:
\[ 5x + 2x + 5 = 7x + 5 \]
Now, we have:
\[ 7x - 3 = 7x + 5 \]
Next, subtract \( 7x \) from both sides:
\[ -3 = 5 \]
This statement is false. Since we reached a contradiction, it indicates that there are **no solutions** to the equation.
Therefore, the best description of the number of solutions for the given equation is that there are **no solutions**.
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