Question

an inequality is a mathematical sentence that uses symbols to compare two expressions. word - sentences can be written as inequalities. a number is at least 12.→m≥12. inequalities can be written as word sentences. x - 4<3→a number minus 4 is less than 3. inequalities with variables are open sentences; they are neither true nor false. when a value is substituted for the variable, the inequality becomes a closed sentence; then the inequality is true or false for that value. remember: inequality symbols < is less than > is greater than ≠ is not equal to ≤ is less than or equal to ≥ is greater than or equal to represent each situation by an inequality. (hint: use any variable to represent a number.) 1. 2 is less than a number. 2 < d 2. the temperature is no more than - 15°f. 3. 5 is not equal to the sum of a number and 2. 4. three times a number does not exceed 50. 5. triple a value is less than or equal to 20. 6. a number minus 7 is greater than or equal to 2. 7. the sum of n and 3 is greater than or equal to 6. 8. one fifth of the band members is more than 18. write each inequality as a word sentence. 9. 6 > m 6 is greater than m. 10. z≤32 11. y≠5 12. - 12≠t 13. x + 3≥4 14. 43 > - 2p 15. |v|>9 16. 6 > b÷19 17. t - 12≥ - 20 18. 16 > c÷12 19. 89 > e÷(-7) 20. \frac{n}{-9}≤ - 4 sourcebook lesson 3 - 1, pages 54 - 55. chapter 3

Explanation:

Step1: Translate word - sentences to inequalities

2. Let the temperature be $t$. "No more than" means $\leq$.

$t\leq - 15$

3. Let the number be $x$. The sum of a number and 2 is $x + 2$. "Not equal to" is $

eq$.
$5
eq x + 2$

4. Let the number be $y$. "Three times a number" is $3y$, "does not exceed" means $\leq$.

$3y\leq50$

5. Let the value be $z$. "Triple a value" is $3z$, "less than or equal to" is $\leq$.

$3z\leq20$

6. Let the number be $a$. "A number minus 7" is $a - 7$, "greater than or equal to" is $\geq$.

$a - 7\geq2$

7. Given the expression with $n$.

$n + 3\geq6$

8. Let the number of band - members be $b$. "One fifth of the band members" is $\frac{1}{5}b$, "more than" means $>$.

$\frac{1}{5}b>18$

Step2: Translate inequalities to word - sentences

10. $z\leq32$: $z$ is less than or equal to 32.

11. $y

eq5$: $y$ is not equal to 5.

12. $- 12

eq t$: Negative 12 is not equal to $t$.

13. $x + 3\geq4$: The sum of $x$ and 3 is greater than or equal to 4.

14. $43>-2p$: 43 is greater than negative 2 times $p$.

15. $|v|>9$: The absolute value of $v$ is greater than 9.

16. $6>b\div19$: 6 is greater than $b$ divided by 19.

17. $t - 12\geq - 20$: $t$ minus 12 is greater than or equal to negative 20.

18. $16>c\div12$: 16 is greater than $c$ divided by 12.

19. $89>e\div(-7)$: 89 is greater than $e$ divided by negative 7.

20. $\frac{n}{-9}\leq - 4$: $n$ divided by negative 9 is less than or equal to negative 4.

Answer:

1. $t\leq - 15$
2. $5

eq x + 2$

1. $3y\leq50$
2. $3z\leq20$
3. $a - 7\geq2$
4. $n + 3\geq6$
5. $\frac{1}{5}b>18$
6. $z$ is less than or equal to 32.
7. $y$ is not equal to 5.
8. Negative 12 is not equal to $t$.
9. The sum of $x$ and 3 is greater than or equal to 4.
10. 43 is greater than negative 2 times $p$.
11. The absolute value of $v$ is greater than 9.
12. 6 is greater than $b$ divided by 19.
13. $t$ minus 12 is greater than or equal to negative 20.
14. 16 is greater than $c$ divided by 12.
15. 89 is greater than $e$ divided by negative 7.
16. $n$ divided by negative 9 is less than or equal to negative 4.