Which Of The Following Is A True Solution

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"Which of the following is a true solution to the equation 2x + 5 = 15? "
with options like A) x=3, B) x=5, C) x=10, D) x=0,
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Assuming the complete multiple‑choice question is:

Which of the following is a true solution to the equation 2x + 5 = 15?

A) x = 3
B) x = 5
C) x = 10
D) x = 0

In this article we will examine each option, demonstrate how to solve the equation step‑by‑step, verify the correct answer, and highlight common pitfalls that students often encounter. By the end, you will have a clear, repeatable method for tackling similar linear equations and a solid understanding of why the correct choice is the only one that satisfies the original statement.

1. Understanding the structure of the equation

The expression 2x + 5 = 15 is a first‑degree linear equation in one variable. So its goal is to find the value of x that makes the left‑hand side equal to the right‑hand side. The standard approach is to isolate x through a series of algebraic manipulations that preserve equality.

2. Solving the equation

Step 1 – Subtract 5 from both sides
2x + 5 − 5 = 15 − 5
2x = 10

Step 2 – Divide both sides by 2
2x / 2 = 10 / 2
x = 5

Thus the mathematical solution is x = 5. Any answer that does not equal 5 cannot be a true solution.

3. Evaluating the answer choices

• Option A (x = 3)
  Substituting 3 into the original equation: 2(3) + 5 = 6 + 5 = 11, which is not 15. Which means, A is incorrect.

• Option B (x = 5)
  Substituting 5 gives: 2(5) + 5 = 10 + 5 = 15, matching the right‑hand side exactly. B satisfies the equation, so it is the true solution.

• Option C (x = 10)
  Substituting 10 yields: 2(10) + 5 = 20 + 5 = 25, which exceeds 15. C is therefore incorrect.

• Option D (x = 0)
  Substituting 0 produces: 2(0) + 5 = 0 + 5 = 5, far from 15. D does not solve the equation.

4. Verification techniques

While substitution is the simplest check, you can also employ the “balance” method: after each manipulation, check that both sides remain equal. For this problem:

1. Start with 2x + 5 = 15.2. Subtract 5 → 2x = 10 (still balanced).
2. Divide by 2 → x = 5 (equality preserved).

If you back‑substitute x = 5 into the original form, the balance is restored, confirming correctness.

5. Common mistakes and how to avoid them

1. Skipping the subtraction step – Some learners try to divide directly, which leads to fractions or errors. Always isolate the term containing x first.
2. Mishandling signs – When moving terms across the equals sign, the sign changes. Forgetting to change the sign of 5 when subtracting can produce an incorrect intermediate result.
3. Arithmetic errors – Simple mental math mistakes (e.g., 15 − 5 = 10) are easy to make. Writing each step on paper or using a calculator helps maintain accuracy.
4. Assuming multiple solutions – Linear equations of the form ax + b = c have exactly one solution. Recognizing this prevents the search for non‑existent extra answers.

6. Generalizing the method

The steps used here are universally applicable to any linear equation with a single variable:

Want to learn more? We recommend if jk and lm which statement is true and 14 of 25 is what percent for further reading.

1. Collect like terms on one side (often by adding or subtracting constants).
2. Factor out the coefficient of x if necessary.
3. Divide or multiply to isolate x.
4. Verify by substitution.

Applying this framework to problems such as 3x − 7 = 8 or 5 − 4x = 2 will yield correct solutions with confidence.

7. Why the other options fail in a broader context

Even though the question is framed as a multiple‑choice test, the underlying principle is that a “true solution” must satisfy the original equation without any approximation. Options that produce a different numeric value on the left‑hand side violate this fundamental requirement, rendering them false regardless of how closely they resemble the correct answer.

8. Conclusion

The equation 2x + 5 = 15 has a single, unequivocal solution: x = 5. So among the presented choices, only option B meets this criterion. In real terms, by following a systematic approach—subtracting constants, isolating the variable, and verifying through substitution—students can solve similar linear equations efficiently and avoid common errors. This method not only answers the specific multiple‑choice question but also equips learners with a reliable tool for tackling a wide range of algebraic problems.

9. Real‑world applications

Linear equations of the form ax + b = c appear frequently in everyday situations. Here's a good example: calculating the number of items you can purchase with a fixed budget, determining the time required to travel a given distance at a constant speed, or figuring out the break‑even point in a simple profit‑loss model all reduce to solving a single‑variable linear equation. By mastering the balance‑method steps — isolating the variable term, performing inverse operations, and checking the result — you gain a quick, reliable tool for these practical problems.

10. Practice problems to reinforce the technique

1.4x − 9 = 23
2.7 + 3x = −2
3. −5x + 12 = 2
4. (½)x + 4 = 10

Work through each using the four‑step framework: (i) move constants to one side, (ii) combine like terms, (iii) divide by the coefficient of x, and (iv) substitute back to verify. Consistent practice builds intuition and reduces the likelihood of the common errors highlighted earlier.

11. Final thoughts

The balance method is more than a mechanical recipe; it embodies the fundamental principle of equality that underlies all algebra. By continually checking that both sides of an equation remain equal after each manipulation, you safeguard against sign slips, arithmetic slips, and premature shortcuts. This disciplined approach not only yields the correct solution for 2x + 5 = 15 but also equips you to tackle any linear equation — whether it appears on a test, in a homework assignment, or in a real‑world scenario — with confidence and accuracy.

In short, treat every algebraic step as a balance check, isolate the variable systematically, and always verify your answer. Doing so transforms solving linear equations from a guess‑and‑check chore into a reliable, repeatable skill.

The balance method's power extends beyond simple equations. When students internalize this approach, they develop algebraic thinking that serves them well in more advanced mathematics. The discipline of maintaining equality at each step builds logical reasoning skills transferable to geometry, calculus, and beyond.

On top of that, the verification step—substituting the solution back into the original equation—reinforces the concept that mathematics is self-correcting. This habit of double-checking work becomes invaluable in fields like engineering, finance, and scientific research where precision is key.

The equation 2x + 5 = 15, while straightforward, exemplifies how systematic problem-solving transforms complexity into clarity. Each algebraic manipulation follows logically from the previous step, creating an unbroken chain of reasoning that leads inevitably to the correct answer.

By mastering this technique and applying it consistently across various contexts, students don't just learn to solve equations—they learn to think mathematically. This foundation proves essential as they encounter increasingly sophisticated mathematical challenges in their academic and professional journeys.