Final answer:
Statement a) is true for some values of x, specifically when x=4, and statement b) is false for all values of x because the equation does not balance after simplification.
Step-by-step explanation:
For each statement about the value of x, we need to determine whether it is true for all, some, or none of the values of x. Let's consider each statement one by one.
Statement a) 3x = x + 8
To determine if this statement is always true, sometimes true, or never true, we need to simplify the equation by isolating x. Subtract x from both sides to get: 2x = 8
Divide both sides by 2 to get: x = 4
This equation is true for some value of x, specifically when x is 4.
Statement b) 2(x - 5) = 2x - 5
For b), let's distribute 2 into the parenthesis: 2x - 10 = 2x - 5
If we try to simplify this equation, we'll find that subtracting 2x from both sides gives us: -10 ≠ -5
This statement is false for all values of x because the left and the right sides do not equal each other after simplifying the equation.
In conclusion, statement a) is true for some values of x, specifically x = 4, and statement b) is false for all values of x.