Bihar School Examination Board (BSEB) Class 8 Mathematics: Linear Equations in One Variable

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Linear Equations in One Variable

   1.

   What is the solution for the equation $x + 5 = 12$?

   1. (A)

      $x = 7$

   2. (B)

      $x = 5$

   3. (C)

      $x = 17$

   4. (D)

      $x = -7$

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   Answer: (A)

   $x = 7$

   To solve for $x$, subtract 5 from both sides of the equation: $x + 5 - 5 = 12 - 5$, which simplifies to $x = 7$.

   Linear Equations in One Variable · Easy

2. 2.

   Solve for $y$: $3y - 8 = 10$.

   1. (A)

      $y = 4$

   2. (B)

      $y = 2$

   3. (C)

      $y = 6$

   4. (D)

      $y = 18$

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   Answer: (C)

   $y = 6$

   First, add 8 to both sides: $3y - 8 + 8 = 10 + 8$, which gives $3y = 18$. Then, divide by 3: $y = 18 / 3$, so $y = 6$.

   Linear Equations in One Variable · Medium

3. 3.

   The sum of two consecutive integers is 45. What is the smaller integer?

   1. (A)

      21

   2. (B)

      22

   3. (C)

      23

   4. (D)

      24

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   Answer: (B)

   22

   Let the smaller integer be $x$. The next consecutive integer is $x + 1$. Their sum is $x + (x + 1) = 45$. This simplifies to $2x + 1 = 45$. Subtract 1 from both sides to get $2x = 44$, then divide by 2 to find $x = 22$.

   Linear Equations in One Variable · Hard

4. 4.

   If $\frac{x}{4} + 2 = 6$, what is the value of $x$?

   1. (A)

      24

   2. (B)

      8

   3. (C)

      16

   4. (D)

      4

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   Answer: (C)

   16

   First, subtract 2 from both sides: $\frac{x}{4} = 6 - 2$, so $\frac{x}{4} = 4$. Then, multiply both sides by 4: $x = 4 \times 4$, which gives $x = 16$.

   Linear Equations in One Variable · Medium

5. 5.

   A number when multiplied by 5 and then decreased by 7 gives 13. What is the number?

   1. (A)

      5

   2. (B)

      3

   3. (C)

      2

   4. (D)

      4

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   Answer: (D)

   4

   Let the number be $n$. The problem can be written as the equation $5n - 7 = 13$. Add 7 to both sides: $5n = 20$. Divide by 5: $n = 4$.

   Linear Equations in One Variable · Hard

— End of the paper · updated 14 October 2026 —