Solve the equation:

\[\frac{1}{4}(3c+5) - \frac{1}{2}(2c+3) = \frac{1}{2}\]

Please show your work to help understand the solution process.

So,
1/4(3c + 5) + -1/2(2c + 3) = 1/2
First, we distribute to get rid of the parentheses. (PEMDAS) 3/4c + 1 1/4 - c - 1 1/2 = 1/2
Now, we collect like terms. -1/4c - 1/4 = 1/2
Add 1/4 to both sides. -1/4c = 3/4
Now, multiply by the reciprocal (-4/1). c = -3
Check your answer.
1/4(3[-3] + 5) + -1/2(2[-3] + 3) = 1/2
1/4(-9 + 5) + -1/2(-6 + 3) = 1/2
-2 1/4 + 1 1/4 + 3 - 1 1/2 = 1/2
-1 + 1 1/12 = 1/2
1/2 = 1/2

Answered by SchwarzschildRadius | 2024-06-10

1/4(3c+5)-1/2(2c+3)=1/23/4c+1u1/4-1c-1u1/2=1/2 3/4c-1c=-1/4c 1u1/4-1u1/2=-1/4 -1/4c-1/4=1/2 +1/4 +1/4 -1/4c=3/4 /-1/4 /-1/4 answer: -3

Answered by wiktoriajablonska | 2024-06-10

We solved the equation 4 1 ​ ( 3 c + 5 ) − 2 1 ​ ( 2 c + 3 ) = 2 1 ​ by multiplying through to eliminate fractions, distributing, combining like terms, and isolating the variable. The solution is c = − 3 , which was verified by substituting back into the original equation. Hence, the final answer is c = − 3 .
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Answered by SchwarzschildRadius | 2024-12-26