Inequalities

10 Grade 6 Mathematics questions on Inequalities, with worked marking schemes. 10 questions are available on this topic in full.

1. Question 1

   1 mark

   Which symbol means 'less than'?

   A. ≤

   B. >

   C. ≥

   D. <

   (1 mark)

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2. Question 2

   1 mark

   Solve: $x+3>7$

   A. x > 3

   B. x > 4

   C. x < 4

   D. x > 10

   (1 mark)

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3. Question 3

   1 mark

   The largest whole number satisfying $x<6$ is:

   A. 4

   B. 7

   C. 6

   D. 5

   (1 mark)

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4. Question 4

   1 mark

   Which value satisfies $2x\le 10$?

   A. 6

   B. 7

   C. 8

   D. 4

   (1 mark)

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5. Question 5

   1 mark

   Solve: $3x-1<8$

   A. x > 3

   B. x < 3

   C. x < 9

   D. x < 7

   (1 mark)

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6. Question 6

   1 mark

   Solve: $4x+2\ge 18$

   A. x ≤ 4

   B. x ≥ 20

   C. x ≥ 4

   D. x ≥ 5

   (1 mark)

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7. Question 7

   1 mark

   Solve: $-2x>-8$

   A. x > 4

   B. x < −4

   C. x < 4

   D. x > −4

   (1 mark)

   Marking scheme

   C. $x<4$ — divide both sides by $-2$. Dividing by a negative number reverses the inequality, so $>$ becomes $<$. A is exactly what happens if that rule is forgotten.

8. Question 8

   1 mark

   List the whole numbers satisfying $2\le x<7$.

   A. 1, 2, 3, 4, 5, 6

   B. 3, 4, 5, 6

   C. 2, 3, 4, 5, 6, 7

   D. 2, 3, 4, 5, 6

   (1 mark)

   Marking scheme

   D. $2,3,4,5,6$ — the $\le$ includes $2$ but the $<$ excludes $7$. C wrongly includes $7$ and B wrongly excludes $2$; the two signs are different and that is the whole question.

9. Question 9

   1 mark

   Write in symbols: 'y is greater than or equal to 5'.

   A. y ≤ 5

   B. y ≥ 5

   C. y = 5

   D. y > 5

   (1 mark)

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10. Question 10

    1 mark

    Solve: $5-x>2$

    A. x < 3

    B. x < 7

    C. x > 7

    D. x > 3

    (1 mark)

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