STEPf
Okay, so I need to figure out how to solve this problem: Find the value of x in the equation 3x + 5 = 20. Hmm, let's see. Alright, starting with the basics. I remember that to solve for x, I need to isolate it on one side of the equation. The equation here is 3x plus 5 equals 20.
First, maybe I should get rid of that 5 that's being added to the 3x. To do that, I can subtract 5 from both sides of the equation. That way, I keep the equation balanced. Let me write that down:
3x + 5 - 5 = 20 - 5
Simplifying both sides, the +5 and -5 on the left side cancel each other out, leaving just 3x. On the right side, 20 minus 5 is 15. So now the equation is 3x = 15.
Alright, now I need to get x by itself. Since 3 is multiplied by x, I should do the opposite operation, which is division. So I'll divide both sides by 3. Let me check that:
https://www.18122.com/url/usdt/usdt1508.jpg
3x / 3 = 15 / 3
On the left side, 3 divided by 3 is 1, so it's just x. On the right side, 15 divided by 3 is 5. So x equals 5.
Wait, let me verify if that's correct. If I plug x = 5 back into the original equation, does it hold true? Let's see:
3*(5) + 5 = 15 + 5 = 20. Yep, that's exactly the right side of the equation. So that checks out.
But wait, did I make any mistakes in my 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. Seems straightforward.
Is there another way to approach this problem? Maybe by isolating x differently? Let's think. Alternatively, could I first divide both sides by 3? Let's try that:
(3x +5)/3 =20/3
That gives x + 5/3 = 20/3. Then subtract 5/3 from both sides: x =20/3 -5/3 =15/3=5. Same result. So either method works.
Hmm, so both methods lead to x=5. That gives me more confidence that the answer is correct.
Another thing to consider: sometimes when solving equations, especially with multiple steps, it's easy to make sign errors or arithmetic mistakes. Let me double-check the arithmetic.
Original equation: 3x +5=20. Subtract 5: 20-5 is 15. Then 15 divided by 3 is 5. Correct.
Plugging back in: 3*5 is 15, plus 5 is 20. Perfect.
I think that's solid. Maybe I can visualize this on a number line or something. Let's see. If 3x is 15, then each x is a third of that. So splitting 15 into three equal parts gives 5 each. Yeah, that makes sense.
Alternatively, thinking in terms of inverse operations. The equation is saying that when you multiply a number by 3 and then add 5, you get 20. To reverse that, you subtract 5 first (undoing the addition) and then divide by 3 (undoing the multiplication).
So step-by-step, reversing the operations: starting from 20, subtract 5 to get 15, then divide by 3 to get 5. Exactly the same as before.
Is there a way this could be a trick question? Maybe if the equation had variables on both sides or something, but here it's straightforward. The operations are clearly addition and multiplication, so standard inverse operations apply.
Wait, another thought: sometimes people confuse the order of operations when solving equations. For example, if there were parentheses or exponents, you have to be careful. But here, it's just multiplication and addition. According to PEMDAS, multiplication comes before addition, but when solving, we do the reverse: undo addition first, then multiplication.
So in this case, since the equation is 3x +5 =20, the order of operations when evaluating would be multiply x by 3, then add 5. To solve, we reverse those steps: subtract 5 first, then divide by 3.
That's exactly what I did. So that's correct.
I guess another common mistake could be subtracting 3 instead of dividing by 3. But no, because 3 is a coefficient, not a term. If it were 3 + x =20, then subtracting 3 would be correct. But here it's 3 times x, so division is needed.
Let me also think about real-world context. Suppose you have 3 groups of x apples, and you add 5 more apples, totaling 20 apples. How many apples are in each group? So you take away the 5 extra apples, leaving 15 apples in 3 groups, so 5 per group. That makes sense.
Or maybe money: if you have 3 times some amount of money plus 5 equals 20, how much is that amount? Take away 5, you have 15, which is 3 times the amount, so the amount is $5.
All these analogies point to the same answer.
I think I've covered different angles here. The solution seems consistent across different methods and checks out when substituting back into the original equation. No mistakes detected in the process. So yeah, x equals 5 is the correct answer.
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
]
The left side equals the right side, confirming the solution is correct.
Answer: (\boxed{5})
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