Sharp

CasinoGames

Okay, so I need to figure out how to solve this problem where I have to find the value of x in the equation 3x + 5 = 17. Let me start by recalling what I know about algebra. The goal is to isolate x on one side of the equation, right?


First, I remember that to solve for x, I should get rid of the constant term on the left side. The equation is 3x + 5 = 17. The 5 is being added to 3x, so the opposite operation would be subtraction. That means I should subtract 5 from both sides to keep the equation balanced. Let me write that down:


3x + 5 - 5 = 17 - 5


Simplifying both sides, the +5 and -5 on the left cancel each other out, leaving just 3x. On the right side, 17 minus 5 is 12. So now the equation is 3x = 12.


Now, I need to get x by itself. Since 3 is multiplied by x, the opposite operation is division. So I should divide both sides by 3. Let me do that:


3x / 3 = 12 / 3


On the left side, 3 divided by 3 is 1, so it's just x. On the right side, 12 divided by 3 is 4. Therefore, x equals 4.


Wait, let me check if that makes sense. If I plug x = 4 back into the original equation, does it hold true? Let's see:


3*(4) + 5 = 12 + 5 = 17. Yes, that's equal to the right side of the equation, which is 17. So that checks out.


Hmm, but what if I made a mistake in the steps? Let me go through it again. Starting with 3x + 5 = 17. Subtract 5 from both sides: 3x = 12. Then divide by 3: x = 4. Yep, same result. And the substitution works.


I guess another way to think about it is to reverse the operations. If 3x + 5 = 17, then 3x must be what you get when you subtract 5 from 17, which is 12. Then x is a third of that, which is 4.


Is there another method? Maybe using algebraic tiles or something? Well, if I imagine the equation as having 3 x-tiles and 5 unit tiles on one side, and 17 unit tiles on the other, I would remove 5 unit tiles from both sides to get 3 x-tiles equal to 12 unit tiles. Then each x-tile is worth 4 units. That also gives x = 4.


Alternatively, could I use inverse operations step by step? Let's see. The equation is 3x + 5 = 17. The last operation done on x is adding 5, so first subtract 5 from both sides: 3x = 12. Then, the operation before that was multiplying by 3, so divide by 3: x = 4. Same answer.


I think that's solid. Maybe I can also graph both sides of the equation to see where they intersect. The left side is a linear function y = 3x + 5, and the right side is a constant function y = 17. The intersection point would be at x = 4, y = 17. Plotting that, when x is 4, y is indeed 17 on both lines. So that confirms it again.


Wait, another check: suppose x was something else, like 3. Then 33 +5 = 14, which is less than 17. If x was 5, 35 +5 = 20, which is more than 17. So 4 is in between, and since 3*4 +5 = 17, that's correct.


Is there a way this could be a trick question? Maybe if the equation was different, but as it stands, it's straightforward. No variables in denominators, no absolute values or anything. Just a simple linear equation.


I think I'm confident that x = 4 is the correct solution. All the checks I did confirm it. So unless I made some arithmetic mistake, which I don't think I did, that's the answer.




To solve the equation (3x + 5 = 17) for (x):



Subtract 5 from both sides to isolate the term with (x):
[
3x + 5 - 5 = 17 - 5 \implies 3x = 12
]



Divide both sides by 3 to solve for (x):
[
\frac{3x}{3} = \frac{12}{3} \implies x = 4
]




Verification:

Substitute (x = 4) back into the original equation:
[
3(4) + 5 = 12 + 5 = 17
]
The left side equals the right side, confirming the solution is correct.


Answer: (\boxed{4})


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