Question

find the solution set. then indicate whether the equation is conditional, an identity, or a contradiction.\\(16(x - 1) = -8(2 - x) + 8x\\)\\(\\)\\(\\)select the correct choice below and fill in any answer boxes present in your choice.\\(\\)\\(\circ\\) a. the solution set is \\(\\{\\ \\}\\)\\(\\)\\(\circ\\) b. the solution is the set of all real numbers.\\(\\)\\(\circ\\) c. the solution is the empty set.

Explanation:

Step1: Expand both sides

Expand the left - hand side: \(16(x - 1)=16x-16\)
Expand the right - hand side: \(-8(2 - x)+8x=-16 + 8x+8x=-16 + 16x\)
So the equation becomes \(16x-16=-16 + 16x\)

Step2: Simplify the equation

Subtract \(16x\) from both sides of the equation \(16x-16=-16 + 16x\)
We get \((16x-16x)-16=(-16)+(16x - 16x)\)
Which simplifies to \(-16=-16\)

Since the equation \(-16 = - 16\) is always true for any real number \(x\), the solution of the equation is the set of all real numbers. And an equation that is true for all real numbers is called an identity.

Answer:

B. The solution is the set of all real numbers.