Question

solve the equation. then determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
\\(5x + 10 = 10(x + 1) - 5x\\)
what is the solution? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\\(\bigcirc\\) a. the equation has a single solution. the solution set is \\(\\{\\ \\}\\).
\\(\bigcirc\\) b. the solution set is \\(\\{x|x\text{ is a real number}\\}\\).
\\(\bigcirc\\) c. the solution set is \\(\varnothing\\).

Explanation:

Step1: Expand right-hand side

$10(x+1)-5x = 10x + 10 - 5x$

Step2: Simplify right-hand side

$10x + 10 - 5x = 5x + 10$

Step3: Compare both sides

Left-hand side: $5x + 10$; Right-hand side: $5x + 10$
Both sides are identical, so all real numbers satisfy the equation.

Answer:

B. The solution set is {x | x is a real number}

Additionally, this equation is an identity, as it is true for all real values of $x$.