To determine the number of solutions for the equation [tex]\( 2(x+4) - 1 = 2x + 7 \)[/tex], follow these steps:
1. Expand and simplify the equation:
[tex]\[ 2(x+4) - 1 = 2x + 7 \][/tex]
First, distribute the 2 on the left side:
[tex]\[ 2x + 8 - 1 = 2x + 7 \][/tex]
Simplify the left side:
[tex]\[ 2x + 7 = 2x + 7 \][/tex]
2. Compare both sides of the equation:
After simplifying, we have:
[tex]\[ 2x + 7 = 2x + 7 \][/tex]
3. Analyze the equation:
The equation [tex]\( 2x + 7 = 2x + 7 \)[/tex] is always true, regardless of the value of [tex]\( x \)[/tex]. This means that [tex]\( x \)[/tex] can be any real number.
4. Conclusion:
Since the equation holds true for any [tex]\( x \)[/tex], this equation has an infinite number of solutions.
Given the analysis above, the correct answer is:
A. infinite
