Final answer:
The solution involves clearing the equation of fractions, rearranging terms to isolate the variable c, and then solving for c by dividing both sides by 9 to obtain c = 80/9.
Step-by-step explanation:
The student is asking for help solving a linear equation. To assist with this mathematics problem, it's crucial to use algebraic methods to isolate the variable c. Here is the step-by-step solution:
Given:
3/8 c − 2 = 3/2 c − 12
First, let's clear the fractions by multiplying every term by 8 to get rid of the denominators:
8(3/8 c) − 8(2) = 8(3/2 c) − 8(12)
Which simplifies to:
3c − 16 = 12c − 96
Next, subtract 3c from both sides to move all terms with c to one side:
− 16 = 9c − 96
Now, add 96 to both sides to isolate the c term:
80 = 9c
Finally, divide both sides by 9 to get the value of c:
c = 80 / 9