Question

(Multi-step linear equations)

Solve \(\frac{3}{4}c - 1 = 1 + \frac{3}{4}c\).
- a. \(c = \frac{8}{6}\)
- b. \(c = \frac{3}{4}\)
- c. No solution
- d. Infinite solutions

Answer 1

To solve the equation, equal terms involving 'c' on both sides cancel out, resulting in -1 = 1, a false statement. Therefore, the equation has no solution.

Step-by-step explanation:

To solve the multi-step linear equation ¾ c - 1 = 1 + ¾ c, we follow these steps:

1. First, we look at both sides of the equation and notice that the terms involving c are identical, with ¾ c on both the left and right side of the equation.
2. By subtracting ¾ c from both sides of the equation to try and isolate the variable c, we see that the terms cancel each other out, leaving us with -1 = 1, which is not true.
3. We thus conclude that there are no values of c that would satisfy this equation, indicating our solution is 'no solution'.

Since the equation simplifies to a false statement and there are no c terms left to solve for, the equation is inconsistent and has no solutions. This means that the answer is (c) No solution.