Select the correct answer. Solve the equation below for
.
A.
B.
C.
D.
The Correct Answer and Explanation is:
We are given the equation: cx−4=7cx – 4 = 7
We are to solve this for xx.
Step-by-Step Solution:
Step 1: Add 4 to both sides to isolate the term with xx: cx−4+4=7+4cx – 4 + 4 = 7 + 4 cx=11cx = 11
Step 2: Divide both sides by cc: x=11cx = \frac{11}{c}
Final Answer:
x=11c\boxed{x = \frac{11}{c}}
This corresponds to Option C.
Explanation
To solve a linear equation like cx−4=7cx – 4 = 7, our goal is to isolate the variable xx on one side of the equation using inverse operations. In this equation, xx is multiplied by cc and then reduced by 4. We reverse these steps in the opposite order using algebraic principles.
First, we eliminate the subtraction of 4 by adding 4 to both sides of the equation. This maintains equality while simplifying the left side: cx−4+4=7+4⇒cx=11cx – 4 + 4 = 7 + 4 \Rightarrow cx = 11
Now, the left side consists of just the product cxcx, meaning xx is still not isolated. Since xx is multiplied by cc, we do the inverse operation — division — to isolate xx. Dividing both sides by cc gives: x=11cx = \frac{11}{c}
This result shows that the value of xx depends on cc; as long as c≠0c \neq 0, the solution is valid.
This technique — reversing operations in the correct order — is fundamental in solving algebraic equations. The subtraction was undone first, then the multiplication. Keeping track of the equation balance by performing the same operation on both sides is key to reaching the correct solution.
Thus, the correct answer is Option C: x=11cx = \frac{11}{c}.
