Are the two expressions 2x + 6 and -3x + 2 always equivalent, sometimes equivalent, or never equivalent? Explain how you know. If they are sometimes equivalent, what value for x makes them equivalent?
The two expressions 2x + 6 and -3x + 2 are sometimes equivalent.
To determine this, we can set the two expressions equal to each other and solve for x:
2x + 6 = -3x + 2
Adding 3x to both sides:
2x + 3x + 6 = 2
Combining like terms:
5x + 6 = 2
Subtracting 6 from both sides:
5x = -4
Dividing both sides by 5:
x = -4/5
Therefore, when x = -4/5, the two expressions are equivalent. In all other cases, they are not equivalent.