Question

directions: translate each expression.

1. “the sum of a number and 4.”
2. “the quotient of a number and -2.”
3. “the product of a number and 5.”
4. “the difference of a number and 7.”
5. “a number squared increased by 1”
6. “three less than twice a number”

directions: translate each equation. do not solve!

1. “twice a number divided by 6 is 42.”
2. “two times the sum of number and 5 is 20”
3. “four times the difference of a number and 7 is 32”
4. “one - third of a number is 12 less than the number itself”
5. “ten increased by the quotient of a number and 2 is -15”
6. “one less than the product of a number and 3 is 5 more than the number itself”

directions: translate each inequality.

1. “a number is less than 15”
2. “a number greater than or equal to -3”
3. “a number that is at least 90”
4. “a speed limit of 65 mph”
5. “a number that is no more than 20”
6. “a maximum number of 50”
7. “a minimum number of 10”
8. “a number no less than 25”

Explanation:

Step1: Let the number be \(x\). Translate expressions

1. The sum of a number and 4: \(x + 4\)
2. The quotient of a number and - 2: \(\frac{x}{-2}\)
3. The product of a number and 5: \(5x\)
4. The difference of a number and 7: \(x - 7\)
5. A number squared increased by 1: \(x^{2}+1\)
6. Three less than twice a number: \(2x-3\)

Step2: Translate equations

1. Twice a number divided by 6 is 42: \(\frac{2x}{6}=42\)
2. Two times the sum of a number and 5 is 20: \(2(x + 5)=20\)
3. Four times the difference of a number and 7 is 32: \(4(x - 7)=32\)
4. One - third of a number is 12 less than the number itself: \(\frac{1}{3}x=x - 12\)
5. Ten increased by the quotient of a number and 2 is - 15: \(10+\frac{x}{2}=-15\)
6. One less than the product of a number and 3 is 5 more than the number itself: \(3x-1=x + 5\)

Step3: Translate inequalities

1. A number is less than 15: \(x<15\)
2. A number greater than or equal to - 3: \(x\geq - 3\)
3. A number that is at least 90: \(x\geq90\)
4. A speed limit of 65 mph (assuming speed \(s\)): \(s\leq65\)
5. A number that is no more than 20: \(x\leq20\)
6. A maximum number of 50: \(x\leq50\)
7. A minimum number of 10: \(x\geq10\)
8. A number no less than 25: \(x\geq25\)

Answer:

1. \(x + 4\)
2. \(\frac{x}{-2}\)
3. \(5x\)
4. \(x - 7\)
5. \(x^{2}+1\)
6. \(2x-3\)
7. \(\frac{2x}{6}=42\)
8. \(2(x + 5)=20\)
9. \(4(x - 7)=32\)
10. \(\frac{1}{3}x=x - 12\)
11. \(10+\frac{x}{2}=-15\)
12. \(3x-1=x + 5\)
13. \(x<15\)
14. \(x\geq - 3\)
15. \(x\geq90\)
16. \(s\leq65\)
17. \(x\leq20\)
18. \(x\leq50\)
19. \(x\geq10\)
20. \(x\geq25\)