Final answer:
The given equation after simplification results in a single value for x, which is -9/10. Hence, the equation has a unique solution, indicating answer choice (A) 'One solution' is correct.
Step-by-step explanation:
The question "The equation 1 – 4⁄3x = 1⁄2(–x + 7) has what type of solution set?" is asking us to determine the nature of the solutions for the given equation. To find the type of solution set, we should first attempt to simplify and solve the equation.
We can start by distributing the 1/2 on the right side of the equation:
1 – 4/3x = 1/2 × (–x) + 1/2 × 7
1 – 4/3x = –x/2 + 7/2
Now, let's isolate the terms with x on one side and the constant terms on the other side:
Add 4/3x to both sides:
1 = 4/3x – x/2 + 7/2
To combine the x terms, find a common denominator:
1 = (8/6)x – (3/6)x + 7/2
1 = (5/6)x + 7/2
Now, isolate x by subtracting 7/2 from both sides and then multiplying by the reciprocal of 5/6:
1 – 7/2 = (5/6)x
(–2/2) = (5/6)x
–(3/2) = (5/6)x
Multiply both sides by the reciprocal of 5/6 to solve for x:
x = –(3/2) × (6/5)
x = –(9/10)
Since we obtained a single value for x, the equation has one solution. So, the answer is (A) One solution.