AGENT
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 = 20. Let me start by recalling what I know about algebra. The goal is to isolate x on one side of the equation to find its value.
First, the equation is 3x + 5 = 20. To isolate x, I should get rid of the 5 that's being added to the term with x. The opposite of addition is subtraction, so I think I need to subtract 5 from both sides of the equation. Let me try that.
Subtracting 5 from both sides would look like:
3x + 5 - 5 = 20 - 5
Simplifying both sides, the +5 and -5 on the left side cancel each other out, so I get:
3x = 15
Now, I need to get x by itself. The 3 is multiplied by x, so the opposite operation is division. I should divide both sides by 3. Let me write that down:
3x / 3 = 15 / 3
Simplifying that, the 3's on the left side cancel out, leaving just x, and 15 divided by 3 is 5. So, x = 5.
Wait, let me check if that makes sense. If I plug x = 5 back into the original equation, does it hold true? Let's see:
3*(5) + 5 = 15 + 5 = 20. Yes, that equals 20, which matches the right side of the equation. 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 =20. Subtract 5 from both sides: 3x =15. Then divide by 3: x=5. Yep, same result. And the check works. I think that's correct.
Alternatively, could I have done it another way? Maybe by isolating x first? Let me think. If I divide everything by 3 first, the equation would become x + (5/3) = 20/3. Then subtract 5/3 from both sides: x = 20/3 - 5/3 = 15/3 =5. Same answer. So both methods work.
Another way to verify is to use algebra tiles or a balance method. Imagine a balance scale where both sides have to be equal. On the left, there are three x tiles and five 1-tiles. On the right, there are twenty 1-tiles. To find x, you remove five 1-tiles from both sides, leaving three x tiles on the left and fifteen 1-tiles on the right. Then each x tile is worth five 1-tiles. That makes sense.
I guess there's no other possible solution here because it's a linear equation with only one variable. So x must be 5. I don't see any other possibilities. Unless there's a trick in the question that I'm missing, but it seems straightforward. The problem is probably testing basic algebra skills.
Wait, maybe someone could think that you should subtract 3 first? Let me see. If someone incorrectly subtracts 3 from both sides, they'd get 3x +5 -3 =20 -3, which is 3x +2 =17. Then subtract 2 to get 3x=15, which still leads to x=5. Wait, even if they messed up the first step, as long as they correct it later, they might still get the right answer. But that's not the proper method. The correct first step is to subtract 5, not 3.
Or if someone divides first but makes a mistake in division. For example, dividing 5 by 3 incorrectly. But in my earlier alternative method, I correctly divided 20 by 3 to get approximately 6.666..., then subtracted 5/3 (which is about 1.666...) to get 5. So that works.
Another possible mistake could be in the sign. If someone added 5 instead of subtracting, they'd get 3x =25, leading to x=25/3, which is about 8.333..., but plugging that back in would give 3*(25/3)+5=25+5=30, which is not 20. So that's wrong. So it's important to subtract 5.
I think I've covered the possible ways to approach and verify this problem. The key steps are inverse operations: undoing the addition by subtraction, then undoing the multiplication by division. Checking the solution by substitution confirms it's correct. No other solutions exist for this equation because it's linear and has only one variable.
To solve the equation (3x + 5 = 20) for (x), follow these steps:
Subtract 5 from both sides to isolate the term with (x):
[
3x + 5 - 5 = 20 - 5 \implies 3x = 15
]
Divide both sides by 3 to solve for (x):
[
\frac{3x}{3} = \frac{15}{3} \implies x = 5
]
Verification:
Substitute (x = 5) back into the original equation:
[
3(5) + 5 = 15 + 5 = 20
https://www.18122.com/url/usdt/usdt0942.jpg
]
The left side equals the right side, confirming the solution is correct.
Answer: (x = 5)
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