Linear Inequalities

10 Grade 7 Mathematics questions on Linear Inequalities, with worked marking schemes. 10 questions are available on this topic in full.

1. Question 1

   1 mark

   The largest integer satisfying $4x-3<25$ is:

   A. 28

   B. 7

   C. 6

   D. 5

   (1 mark)

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2. Question 2

   1 mark

   List integers satisfying: $-2<x\le 3$

   A. -2, -1, 0, 1, 2, 3

   B. 0, 1, 2, 3

   C. -1, 0, 1, 2

   D. -1, 0, 1, 2, 3

   (1 mark)

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3. Question 3

   1 mark

   Solve: $3x-5\le 7$

   A. x ≥ 4

   B. x ≤ 2

   C. x ≤ 4

   D. x < 7

   (1 mark)

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4. Question 4

   4 marks

   Solve: $-3\le 2x+1<9$. List the integer values.

   (4 marks)

   Marking scheme

   This is two inequalities in one, so treat the whole chain together. Subtract $1$ from all three parts: $-4\le 2x<8$. (1)

   Divide all three parts by $2$, a positive number, so both signs stay the same: $-2\le x<4$. (1)

   So $x$ is at least $-2$ and strictly less than $4$. (1)

   The integers in that range are $-2$, $-1$, $0$, $1$, $2$, $3$ — note $4$ is excluded. (1)

   Final answer: $-2\le x<4$; integers $-2,-1,0,1,2,3$.

5. Question 5

   3 marks

   A number x satisfies both $x>-1$ and $3x\le 12$. Find the range of x and list the integer values.

   (3 marks)

   Marking scheme

   Take each condition in turn. The first is already solved: $x>-1$. (1)

   For the second, divide $3x\le 12$ by $3$ to get $x\le 4$. (1)

   Both must hold at once, so combine them: $-1<x\le 4$. (1)

   The integers strictly above $-1$ and up to $4$ are $0$, $1$, $2$, $3$, $4$. (1)

   Final answer: $-1<x\le 4$; integers $0,1,2,3,4$.

6. Question 6

   1 mark

   Solve: $5-2x>1$

   A. x > 2

   B. x < 2

   C. x < 3

   D. x > 3

   (1 mark)

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7. Question 7

   2 marks

   Solve: $\frac{x+3}{2}>5$

   (2 marks)

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8. Question 8

   1 mark

   Which value does NOT satisfy $2x+1<9$?

   A. 4

   B. 3

   C. 0

   D. 2

   (1 mark)

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9. Question 9

   3 marks

   Solve the inequality and represent on a number line: $3x-5\le 7$

   (3 marks)

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10. Question 10

    1 mark

    Solve: $\frac{x}{4}\ge 3$

    A. x ≥ 7

    B. x ≤ 12

    C. x ≥ $\frac{3}{4}$

    D. x ≥ 12

    (1 mark)

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