Question

1. \four times the difference of a number and 7 is 32\
2. \one-third of a number is 12 less than the number itself\
3. \ten increased by the quotient of a number and 2 is -15\
4. \one less than the product of a number and 3 is 5 more than the number itself\

directions: translate each inequality,

1. \a number 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:

Problem 9:

Step1: Define the variable

Let the number be \( x \). The difference of the number and 7 is \( x - 7 \).

Step2: Translate the phrase

Four times the difference is \( 4(x - 7) \), and this equals 32. So the equation is \( 4(x - 7)=32 \).

Step1: Define the variable

Let the number be \( x \). One - third of the number is \( \frac{1}{3}x \).

Step2: Translate the phrase

"12 less than the number itself" is \( x - 12 \). So the equation is \( \frac{1}{3}x=x - 12 \).

Step1: Define the variable

Let the number be \( x \). The quotient of the number and 2 is \( \frac{x}{2} \).

Step2: Translate the phrase

Ten increased by this quotient is \( 10+\frac{x}{2} \), and this equals - 15. So the equation is \( 10+\frac{x}{2}=-15 \).

Answer:

\( 4(x - 7)=32 \)

Problem 10: