To solve this equation and determine whether it has one solution, no solution, or is an identity, let's simplify and solve it step by step:
21(x + 1) - 6x = 4(2z + 12)
First, distribute the constants on both sides of the equation:
21x + 21 - 6x = 8z + 48
Now, combine like terms on both sides:
(21x - 6x) + 21 = 8z + 48
15x + 21 = 8z + 48
Next, isolate the variables x and z:
15x + 21 = 8z + 48
Subtract 21 from both sides to isolate 15x:
15x = 8z + 48 - 21
15x = 8z + 27
Now, divide both sides by 15 to solve for x:
x = (8z + 27) / 15
So, the equation is not an identity, and it has one solution, which is x = (8z + 27) / 15.