Linear Equations & Inequalities

Practise Linear Equations & Inequalities for FBISE Grade 9–10 Mathematics (Grade 9–10): 6 multiple-choice questions with instant checking and worked explanations. Free, no sign-up.

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1. Question 1

   The line $3x-4y=12$ is parallel to which of the following lines?
   • A$y=\frac{3}{4}x+1$
   • B$y=\frac{4}{3}x-2$
   • C$y=-\frac{3}{4}x+5$
   • D$y=-\frac{4}{3}x+3$
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   Answer: A) $y=\frac{3}{4}x+1$

   Putting the equation in slope‑intercept form gives $y=\frac{3}{4}x-3$, so any line with slope $\frac{3}{4}$ is parallel. Only $y=\frac{3}{4}x+1$ has that slope.

2. Question 2

   Which inequality correctly represents the solution set $-2<x\le 5$?
   • A$-2\le x<5$
   • B$x\ge -2$ and $x\le 5$
   • C$x>-2$ and $x\le 5$
   • D$-2<x<5$
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   Answer: C) $x>-2$ and $x\le 5$

   The notation $-2<x\le 5$ translates to two separate inequalities: $x$ must be greater than $-2$ (not equal) and less than or equal to $5$. Only "$x>-2$ and $x\le 5$" states this correctly.

3. Question 3

   The solution to $4x=20$ is
   • A4
   • B8
   • C6
   • D5
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   Answer: D) 5

   To solve $4x=20$, isolate $x$ by dividing both sides by 4, giving $x=5$. Hence the correct answer is "5". The option "4" is a common error where a student might mistakenly divide 20 by 5 instead of 4. The option "6" results from adding or mis‑calculating the division rather than performing the correct division.

4. Question 4

   In the equation $y=2x+7$, the coefficient of $x$ is the
   • Aslope
   • By-intercept
   • Cvariable
   • Dconstant term
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   Answer: A) slope

   In the equation $y=2x+7$, the number that multiplies the variable $x$ is called the coefficient of $x$, which is the slope of the line. Therefore the correct answer is "slope". The option "y‑intercept" is incorrect because the y‑intercept is the constant term $7$, not the coefficient of $x$. The option "constant term" is wrong because the constant term is $7$, while the coefficient of $x$ is $2$. The option "variable" is incorrect because it refers to $x$ itself, not to the number $2$ that multiplies it.

5. Question 5

   If $2x-7<3$, which of the following could be the value of $x$?
   • A5
   • B7
   • C6
   • D4
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   Answer: D) 4

   Subtracting 7 from both sides gives $2x<10$, and dividing by 2 yields $x<5$. The only listed value that is less than 5 is 4, so 4 is the correct choice.

6. Question 6

   If $3x-5=2x+7$, what is $x$?
   • A9
   • B10
   • C12
   • D11
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   Answer: C) 12

   Subtract $2x$ from both sides to get $x-5=7$, then add $5$ to obtain $x=12$. This satisfies the original equation, while the other options arise from common arithmetic slips.

More FBISE Grade 9–10 Mathematics topics

• Coordinate Geometry (3)
• Probability & Statistics (8)
• Quadratic Equations (5)
• Real & Complex Numbers (7)
• Sets, Functions & Groups (8)
• Trigonometry (6)