Question

Esmeralda wants to solve for x in the equation 3−2x+1⋅3−2x−3=3−3
. Which of the following answers should she select?(1 point)

x=−4


x=−5±73√8


x=−2


x=14

Answer 1

The equation as typed is ambiguous. I’ll solve the two most likely interpretations — neither gives any of the provided choices, so please check the original formatting.

1) If the expression means 3^{−2x+1} ⋅ 3^{−2x−3} = 3^{−3} (exponents on the 3’s):
- Combine exponents: 3^{(−2x+1)+(−2x−3)} = 3^{−4x−2} = 3^{−3}.
- Equate exponents: −4x − 2 = −3 → −4x = −1 → x = 1/4.
(1/4 is not among the given choices.)

2) If it means (3 − 2x + 1)(3 − 2x − 3) = 3 − 3 (i.e. two linear factors multiplied = 0):
- Simplify factors: (4 − 2x)(−2x) = 0 → −8x + 4x^2 = 0 → 4x(x − 2) = 0 → x = 0 or x = 2.
(neither 0 nor 2 is in the choices.)

3) If it means 3 − 2x + 1⋅3 − 2x − 3 = 3 − 3 (with the 1⋅3 multiplicative and no exponents):
- Evaluate 1⋅3 = 3, so left side = 3 − 2x + 3 − 2x − 3 = 3 − 4x.
- Equation 3 − 4x = 0 → x = 3/4.
(3/4 is not in the choices.)

Please paste the original problem with parentheses or caret (^) for exponents (for example 3^(−2x+1)⋅3^(−2x−3)=3^(−3)), and I’ll pick the correct choice.