Sure, let's solve the given equation step by step:
The equation is:
[tex]\[ 3(x - 7) = -21 + 3x \][/tex]
First, we'll distribute the 3 on the left-hand side:
[tex]\[ 3 \cdot (x - 7) = 3x - 21 \][/tex]
So the equation now looks like this:
[tex]\[ 3x - 21 = -21 + 3x \][/tex]
Next, let's simplify by subtracting [tex]\(3x\)[/tex] from both sides:
[tex]\[ 3x - 21 - 3x = -21 + 3x - 3x \][/tex]
[tex]\[ -21 = -21 \][/tex]
Notice that the [tex]\(3x\)[/tex] terms cancel each other out, leaving us with [tex]\(-21 = -21\)[/tex]. This is a true statement and holds for any value of [tex]\(x\)[/tex].
Since the equation simplifies to a true statement without any specific value of [tex]\(x\)[/tex], it means that the equation has infinite solutions. Any value for [tex]\(x\)[/tex] will satisfy the equation.
So, the correct answer is:
Infinite Solutions
