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\\)

a. the equation has a single solution. the solution set is \\{\\}
b. the solution set is \\{x | x is a real number\\}
c. the solution set is \\(\varnothing\\)
what type of equation is this?
a. an inconsistent equation
b. an identity
c. a conditional equation

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 for all real $x$.

Answer:

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

For the equation type:
B. an identity