Question

The equation 1 – 4∕3x = 1∕2(–x + 7) has what type of solution set?

options:
A). One solution
B). Infinitely many solutions
C). Two solutions
D). No solutions

Answer 1

After simplifying and solving the linear equation 1 – 4/3x = 1/2(–x + 7), we find that the equation has one solution, which is x = 3. Therefore, the correct answer is Option A) One solution.

Step-by-step explanation:

We need to determine the type of solution set for the equation 1 – 4/3x = 1/2(–x + 7). To do this, let's simplify and solve the equation step by step.

1. 
   
3. Multiply both sides of the equation by 6 to eliminate the fractions:
   
   6(1 – 4/3x) = 6(1/2)(–x + 7)
4. 
   
6. Simplify the equation:
   
   6 – 8x = –3x + 21
7. 
   
9. Now, let's move all the terms involving x to one side and the constant terms to the other side:
   
   8x – 3x = 21 – 6
10. 
    
12. Simplify the x terms and the constants:
    
    5x = 15
13. 
    
15. Divide both sides by 5 to solve for x:
    
    x = 3

Since we found a single value for x, the equation has one solution. Thus, the correct answer is Option A) One solution.