Question

For each equation, determine whether the equation is true for all, some, or no values of x.

a. 3x = x + 8
b. 50 = x + 2 + x + x + 2
c. 2(x + 5) = 2x + 5

Answer 1

Equation a is true for some values of x, equation b is true for some values of x, and equation c is not true for any value of x.

Step-by-step explanation:

For equation a, 3x = x + 8, we can simplify it by subtracting x from both sides to get 2x = 8. Since x = 4 makes the equation true, this equation is true for some values of x.

For equation b, 50 = x + 2 + x + x + 2, we can simplify it by combining like terms to get 50 = 4x + 4. By subtracting 4 from both sides and then dividing both sides by 4, we find that x = 11.5. Since the equation is true for this value of x, it is true for some values.

For equation c, 2(x + 5) = 2x + 5, we can distribute 2 to get 2x + 10 = 2x + 5. By subtracting 2x from both sides, we get 10 = 5. Since this is not true, the equation is not true for any value of x.