Question

Determine what value(s) for the variable would make each algebraic equation a true number sentence.

d2 = 36 is true for
A. d = 6
B. d = -6
C. d = 6 or d = -6
D. d = 12

2x - 2 + 3x = 4x is true for
A. x = 0
B. x = 1
C. x = 2
D. x = 3

x + 25 = x - 25 is true for
A. x = 0
B. x = 25
C. x = -25
D. x = any real number

Answer 1

For the first equation, d^2 = 36, the correct answer is C, d = 6 or d = -6. For the second equation, 2x - 2 + 3x = 4x, the correct answer is C, x = 2. For the third equation, x + 25 = x - 25, there is no value of x that makes the equation true.

Step-by-step explanation:

For the equation d^2 = 36 to be true, we need to find the value(s) of d that make the equation valid. By taking the square root of both sides of the equation, we have d = ±6. Therefore, the correct answer is C, d = 6 or d = -6.

For the equation 2x - 2 + 3x = 4x to be true, we need to find the value of x that satisfies the equation. Combining like terms on the left side of the equation, we have 5x - 2 = 4x. By subtracting 4x from both sides of the equation, we get x - 2 = 0. By adding 2 to both sides of the equation, we get x = 2. Therefore, the correct answer is C, x = 2.

For the equation x + 25 = x - 25 to be true, we need to find the value(s) of x that make the equation valid. By simplifying the equation, we have 25 = -25, which is not true. Therefore, the equation is not true for any value of x. The correct answer is D, x = any real number.