Words to Equations - ISEE Lower Level Quantitative Reasoning

1. What equation represents "$4$ fewer than the quantity $2n$ is $12$"?

   $2n-4=12$. Treating 2n as a quantity and subtracting 4, set equal to 12, fits the phrasing.

2. What equation represents "$y$ is less than $10$"?

   $y<10$. The strict inequality $y < 10$ denotes y is below 10 without equality.

3. What equation represents "the difference of $x$ and $9$"?

   $x-9$. Subtracting 9 from x denotes the difference where x is the minuend.

4. What equation represents "twice a number $x$, increased by $7$"?

   $2x+7$. Multiplying x by 2 and adding 7 represents increasing twice the number by 7.

5. What equation represents "$8$ is $3$ more than a number $x$"?

   $8=x+3$. Setting 8 equal to x plus 3 equates 8 to being 3 more than x.

6. What equation represents "$x$ is proportional to $y$ with constant $k$"?

   $x=ky$. Setting x equal to k times y models direct proportionality with constant k.

7. What equation represents "the difference of $9$ and $x$"?

   $9-x$. Subtracting x from 9 denotes the difference where 9 is the minuend.

8. What equation represents "the product of $6$ and a number $x$"?

   $6x$. Multiplying 6 by x expresses the product of the two values.

9. What equation represents "the quotient of a number $x$ and $5$"?

   $\frac{x}{5}$. Dividing x by 5 represents the quotient with x as the dividend.

10. What equation represents "$y$ is at least $10$"?

    $y\ge 10$. The inequality $y \ge 10$ indicates y is 10 or any value greater.

11. What equation represents "$3$ times a number $x$ is $21$"?

    $3x=21$. Multiplying x by 3 and setting equal to 21 equates the product to 21.

12. What equation represents "$7$ less than twice a number $x$"?

    $2x-7$. Multiplying x by 2 and then subtracting 7 captures 7 less than twice the number.

13. What equation represents "the quotient of $5$ and a number $x$"?

    $\frac{5}{x}$. Dividing 5 by x represents the quotient with 5 as the dividend.

14. What equation represents "$3$ times the sum of $x$ and $4$"?

    $3(x+4)$. Parentheses ensure the sum of x and 4 is calculated before multiplying by 3.

15. What equation represents "$5$ more than a number $x$"?

    $x+5$. Adding 5 to x represents a value that is 5 greater than the number x.

16. What equation represents "one-half of a number $x$"?

    $\frac{1}{2}x$. Multiplying x by $\frac{1}{2}$ calculates half of the number x.

17. What equation represents "$7$ less than a number $x$"?

    $x-7$. Subtracting 7 from x expresses a value that is 7 smaller than the number x.

18. What equation represents "$y$ is no more than $10$"?

    $y\le 10$. The inequality $y \le 10$ indicates y is 10 or any value smaller.

19. What equation represents "$4$ fewer than $n$ is $12$"?

    $n-4=12$. Subtracting 4 from n and setting it equal to 12 models the relationship.

20. What equation represents "$4$ fewer than twice $n$ is $12$"?

    $2n-4=12$. Doubling n, subtracting 4, and equating to 12 captures the described operation.

21. What equation represents "a number $x$ is $3$ more than $8$"?

    $x=8+3$. Setting x equal to 8 plus 3 defines x as 3 more than 8.

22. What equation represents "the ratio of $x$ to $4$ is $9$"?

    $\frac{x}{4}=9$. Dividing x by 4 and setting equal to 9 expresses the ratio equaling 9.

23. What equation represents "$y$ is greater than $10$"?

    $y>10$. The strict inequality $y > 10$ denotes y exceeds 10 without equality.

24. What equation represents "the sum of a number $x$ and $5$ is $17$"?

    $x+5=17$. Adding x and 5, then setting equal to 17, represents their sum equaling 17.

25. What equation represents "the sum of $3x$ and $4$"?

    $3x+4$. Adding 4 to the product of 3 and x directly represents their sum.

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