Write and Represent Simple Inequalities - 6th Grade Math

1. Which inequality represents the statement: "$x$ is more than $7$"?

   $x>7$. "More than" translates to the greater than symbol $>$.

2. Which inequality matches this description: "All numbers to the left of $-6$"?

   $x < -6$. "To the left of" means less than on a number line.

3. Which inequality represents the statement: "$x$ is fewer than $12$"?

   $x<12$. "Fewer than" translates to the less than symbol $<$.

4. Which inequality represents "temperature must be above $32$" using $t$?

   $t>32$. "Above" means greater than in mathematical terms.

5. Which inequality represents "a number is less than $-3$" using $x$?

   $x<-3$. "Less than" translates to the $<$ symbol with negative values.

6. Identify the correct inequality for: "At least $10$" (choose $x>10$ or $x<10$).

   Neither; "at least $10$" is $x\ge 10$. "At least" includes the value, requiring $\ge$ not $>$.

7. What inequality represents: "The score $s$ must be under $70$"?

   $s < 70$. "Under" means less than when referring to limits or bounds.

8. What does the inequality $x > 7$ mean in words?

   $x$ is greater than $7$. The symbol $>$ means the value on the left exceeds the value on the right.

9. Identify one integer that is a solution to $x<-1$.

   $-2$. Any integer below $-1$ satisfies the inequality.

10. Which inequality represents "the price must be less than $25$ dollars" using $p$?

    $p<25$. Price constraint uses $<$ for upper limit.

11. Which number line description matches $x < 5$: open circle at $5$ and shading where?

    Open circle at $5$ and shading to the left. Values less than $5$ are to the left on a number line.

12. What does the inequality symbol $<$ mean when comparing $x$ and $c$?

    $x$ is less than $c$. The symbol $<$ indicates the first value is smaller than the second.

13. What can you conclude about the number of solutions to $x>c$ or $x<c$?

    There are infinitely many solutions. All real numbers satisfying the condition form the solution set.

14. Find whether $x=4$ is a solution to $x>4$.

    No, because $4$ is not greater than $4$. Strict inequality excludes the boundary value itself.

15. On a number line, which direction is shaded for the solution set of $x>c$?

    Shade to the right of $c$. Greater than means values increase to the right.

16. What type of dot is used on a number line for $x>c$ or $x<c$ (strict inequality)?

    An open circle at $c$. Open circles exclude the endpoint for strict inequalities.

17. Choose the correct number line description for $x<6$: open circle at $6$, shade left or shade right?

    Open circle at $6$; shade left. For $<$, shade toward smaller values (left on number line).

18. What inequality represents: "The depth $d$ is below $-20$ meters"?

    $d < -20$. "Below" means less than when referring to position or depth.

19. What kind of point marks the boundary for $x>c$ or $x<c$ on a number line?

    An open circle at $c$. Open circles show the boundary value is not included in the solution.

20. What does the inequality $x < -3$ mean in words?

    $x$ is less than $-3$. The symbol $<$ means the value on the left is smaller than the value on the right.

21. Which symbol represents "less than" in an inequality: $<$ or $>$?

    $<$. The arrow opens toward the larger value.

22. Which inequality represents: "You must be older than $13$ years" (let age be $a$)?

    $a>13$. "Older than" means age exceeds the given value.

23. Which inequality represents "you must be older than $13$" using $a$?

    $a>13$. "Older than" means age is greater than the given value.

24. What does the inequality symbol $>$ mean when comparing $x$ and $c$?

    $x$ is greater than $c$. The symbol $>$ indicates the first value exceeds the second.

25. Which symbol represents "less than" in an inequality?

    $<$. The arrow points toward the smaller value.

26. Which inequality matches the solution set shown by shading right of $2$ with an open circle at $2$?

    $x>2$. Shading right with open circle means values greater than boundary.

27. Which set description matches $x<-2$: values greater than $-2$ or values less than $-2$?

    Values less than $-2$. The symbol $<$ means not reaching the given value.

28. Identify the correct inequality for: "At most $10$" (choose $x>10$ or $x<10$).

    Neither; "at most $10$" is $x\le 10$. "At most" includes the value, requiring $\le$ not $<$.

29. Identify one integer that is a solution to $x>5$.

    $6$. Any integer above $5$ satisfies the inequality.

30. What does it mean that $x>c$ has infinitely many solutions?

    There are endlessly many numbers greater than $c$. Any value beyond $c$ satisfies the inequality.

31. Identify the correct inequality for: "At least $10$" (variable $x$).

    Not possible with only $x > c$ or $x < c$; it needs $x \ge 10$. "At least" includes the value itself, requiring $\ge$ not $>$.

32. What does the inequality $x>c$ mean in words?

    $x$ is greater than $c$. The symbol $>$ means the value on the left exceeds the value on the right.

33. Identify the correct inequality for: "No more than $4$" (variable $x$).

    Not possible with only $x > c$ or $x < c$; it needs $x \le 4$. "No more than" includes the value itself, requiring $\le$ not $<$.

34. Which inequality represents "the height must be under $60$ inches" using $h$?

    $h<60$. "Under" means less than in mathematical terms.

35. What direction is shaded on a number line for the solutions to $x < c$?

    Shade to the left of $c$. Values less than $c$ are to the left on a number line.

36. Which symbol represents "greater than" in an inequality: $>$ or $<$?

    $>$. The arrow points toward the smaller value.

37. On a number line, which direction is shaded for the solution set of $x<c$?

    Shade to the left of $c$. Less than means values decrease to the left.

38. Which inequality represents the statement: "The temperature $T$ is above $0$"?

    $T>0$. "Above" means greater than, so use $>$ with the reference value.

39. What inequality represents: "A number $x$ is more than $12$"?

    $x > 12$. "More than" translates to the greater than symbol.

40. Which inequality represents: "A number $n$ is less than $-4$"?

    $n<-4$. Place the variable on the left with $<$ for "less than."

41. Which inequality represents "a number is more than $7$" using $x$?

    $x>7$. "More than" translates to the $>$ symbol.

42. What type of dot is used at $c$ on a number line for $x > c$?

    An open circle at $c$. Open circles exclude the boundary value in strict inequalities.

43. Which inequality models: "The number of pages $p$ read must be less than $50$"?

    $p<50$. "Must be less than" directly translates to $<$.

44. What inequality represents: "You must be older than $13$ years" (age $a$)?

    $a > 13$. "Older than" means age is greater than the given value.

45. Which inequality matches the solution set shown by shading left of $-1$ with an open circle at $-1$?

    $x<-1$. Shading left with open circle means values less than boundary.

46. Identify a value that is a solution to $x<-2$: $-3$, $-2$, or $0$.

    $-3$. Only $-3$ is less than $-2$; others don't satisfy the inequality.

47. Which values are solutions to $x < -1$: $-1$, $-1.5$, $0$, $-10$?

    $-1.5$ and $-10$. Solutions must be strictly less than $-1$.

48. What inequality represents: "A number $x$ is fewer than $5$"?

    $x < 5$. "Fewer than" means less than in mathematical terms.

49. How many solutions does the inequality $x > 2$ have?

    Infinitely many solutions. Any number greater than $2$ is a solution.

50. Which symbol represents "greater than" in an inequality?

    $>$. The arrow points toward the smaller value.

51. Which values are solutions to $x > 4$: $4$, $4.1$, $-2$, $10$?

    $4.1$ and $10$. Solutions must be strictly greater than $4$.

52. What inequality represents: "The temperature $t$ is above $0$"?

    $t > 0$. "Above" means greater than when referring to position or value.

53. Which set description matches $x>3$: values greater than $3$ or values less than $3$?

    Values greater than $3$. The symbol $>$ means exceeding the given value.

54. Which inequality matches this description: "All numbers to the right of $3$"?

    $x > 3$. "To the right of" means greater than on a number line.

55. What does the inequality $x<c$ mean in words?

    $x$ is less than $c$. The symbol $<$ means the value on the left is smaller than the value on the right.

56. Identify a value that is a solution to $x>4$: $3$, $4$, or $5$.

    $5$. Only $5$ is greater than $4$; others don't satisfy the inequality.

57. Which inequality represents the statement: "The depth $d$ is below sea level ($0$)"?

    $d<0$. Below sea level means negative depth, less than zero.

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