Practice Questions
Concept Explanation
A linear equation in one variable has the form ax + b = c, where a ≠ 0. Solving means finding the value of x that makes the equation true.
Method
- Transpose constants to one side and the variable term to the other.
- Divide both sides by the coefficient of x.
- Check by substituting the value back.
Key Form
ax + b = c ⇒ x = (c − b) / a
Example
Solve 3x + 5 = 20. Subtract 5: 3x = 15. Divide by 3: x = 5.
Common Trap
When dividing by a negative coefficient, the inequality sign flips — but in equations, signs cancel correctly if you follow the same operation on both sides.
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Q1 Easy
Find the value of x that satisfies the equation 2x + 3 = 11.
Explanation2x = 8, so x = 4. -
Q2 Easy
Find the value of x that satisfies the equation 5x − 7 = 18.
Explanation5x = 25, so x = 5. -
Q3 Easy
What value of x makes the equation x/4 + 2 = 5 true?
Explanationx/4 = 3, so x = 12. -
Q4 Easy
Find the value of x that satisfies 3(x − 2) = 15.
Explanationx − 2 = 5, so x = 7. -
Q5 Easy
If 4x + 1 = 3x + 9, what is the value of x?
Explanation4x − 3x = 9 − 1, so x = 8. -
Q6 Medium
Find the value of x that satisfies the equation 7 − 2x = 1.
Explanation2x = 6, so x = 3. -
Q7 Medium
What is the value of x in the equation (x + 5)/3 = 4?
Explanationx + 5 = 12, so x = 7.
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Q8 Medium
If 2(3x − 1) = 4x + 6, what is the value of x?
Explanation6x − 2 = 4x + 6, so 2x = 8 and x = 4. -
Q9 Medium
Find the value of x that satisfies the equation 0.5x + 1.5 = 4.
Explanation0.5x = 2.5, so x = 5. -
Q10 Medium
If 5x + 3 = 2x + 18, what is the value of x?
Explanation3x = 15, so x = 5. -
Q11 Hard
What value of x satisfies the equation (2x − 1)/5 + 3 = 6?
Explanation(2x − 1)/5 = 3, so 2x − 1 = 15 and x = 8. -
Q12 Hard
If 3x + 2 = x + 14, what is the value of x?
Explanation2x = 12, so x = 6. -
Q13 Hard
Find the value of x that satisfies 4 − (x + 2)/2 = 1.
Explanation(x + 2)/2 = 3, so x + 2 = 6 and x = 4. -
Q14 Hard
If (5x − 3)/2 = 11, what is the value of x?
Explanation5x − 3 = 22, so 5x = 25 and x = 5.
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DS1 Easy
What is the value of x in the equation 2x + b = 14, where b is a constant?
Statement Ib = 4.
Statement IIx = 5.
ExplanationEach alone: b = 4 gives 2x = 10 so x = 5; Statement II directly gives x = 5. -
DS2 Easy
What is the value of x in the equation ax + 6 = 18, where a is a non-zero constant?
Statement Ia = 3.
Statement IIx = 4.
ExplanationEach alone: a = 3 gives 3x = 12 so x = 4; Statement II gives x = 4 directly.
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DS3 Medium
What is the value of x in the equation (x + k)/2 = 7, where k is a constant?
Statement Ik = 3.
Statement IIx is a positive integer.
ExplanationNeed both: x + 3 = 14 so x = 11; positivity alone does not fix x without k. -
DS4 Medium
What is the value of x in the equation 4x − m = 20, where m is a constant?
Statement Im = 8.
Statement IIx > 4.
ExplanationStatement I alone: 4x = 28 so x = 7. Statement II alone does not give a unique x.