Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
X +1 = 2
The equation has one solution
A value of x that makes the equation true is
which when substituted into the
equation and simplified makes the equation turn into
A value of x that makes the equation false is
, which when substituted into the
equation and simplified makes the equation turn into

The equation x + 1 = 2 has one solution.

If you subtract 1 from both sides, you’ll get one value for x:

x + 1 - 1 = 2 - 1
x = 1

Therefore, the equation has ONE solution. This is the only solution that makes the equation true. If you substitute the value of x into the equation, you’ll get:

x + 1 = 2

( 1 ) + 1 = 2
2 = 2

If you try to substitute x with a different value, it will make the equation false. Let’s say the value of x = 4:

x + 1 = 2
( 4 ) + 1 = 2
5 = 2 ← This is a false statement.

Part 2: A value of x that makes the equation true is 1 (which is the solution), which when substituted into the equation and simplified makes the equation turn into a true statement.

Part 3: A value of x that makes the equation false is any real number other than 1, in which when substituted into the equation and simplified makes the equation turn into a false statement (no solutions).

Therefore, the correct answer is the first option: The equation has ONE solution.

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