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Answer :
Answer: [tex]c=\frac{1}{2}[/tex]
Step-by-step explanation:
To find the solution, we have to solve for c by using inverse properties.
[tex]17c+3(4-2c)=5(7c)[/tex] [multiply]
[tex]17c+12-6c=35c[/tex] [combine like terms]
[tex]11c+12=35c[/tex] [subtract both sides by 11c]
[tex]12=24c[/tex] [divide both sides by 24]
[tex]c=\frac{12}{24}[/tex] [simplify]
[tex]c=\frac{1}{2}[/tex]
So the solution is [tex]c=\frac{1}{2}[/tex].
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Final answer:
The solution to the equation 17c + 3(4 - 2c) = 5(7c) is found by distributing the terms, combining like terms, and solving for c to get the final answer c = 0.5.
Explanation:
The student's question concerns solving a linear equation. To find the solution to 17c + 3(4-2c) = 5(7c), we must distribute and combine like terms. Let's simplify the equation step by step:
Distribute through the parentheses: 17c + 12 - 6c = 35c.
Combine like terms on the left side: 17c - 6c + 12 = 35c, which simplifies to 11c + 12 = 35c.
Subtract 11c from both sides to get the variable terms on one side: 12 = 24c.
Finally, divide both sides by 24 to isolate c: c = 0.5.
Therefore, the final answer to the equation is c = 0.5. The explanation provided includes distribution, combining like terms, and isolating the variable to solve for c.
