Question

to say that |x - 7| ≤ 3 is the same as saying x is in the closed interval a, b where a is 4 and where b is 11. note: you can earn partial credit on this problem. 2 of the questions remain unanswered. problem 10. (1 point) match each word problem statement with its correct algebraic translation. 1. the sum of two consecutive even integers is at least 92. 2. one number is 6 more than twice another. the sum of the numbers is 92. 3. jesse has a total of 92 points on the first 6 quizzes in her sociology class. how many total points must she earn on the remaining 5 quizzes in order to have more than 140 points for the semester? 4. the length of a rectangle is 6 in. more than the width. the perimeter of the rectangle is more than 92 in.

Explanation:

Step1: Translate statement 1

Let the first even integer be $x$, then the next consecutive even integer is $x + 2$. The sum is at least 92, so $x+(x + 2)\geq92$, which simplifies to $2x+2\geq92$.

Step2: Translate statement 2

Let one number be $x$ and the other be $y$. One number is 6 more than twice another, so $y=2x + 6$, and the sum is 92, so $x + y=92$, substituting $y$ gives $x+(2x + 6)=92$.

Step3: Translate statement 3

Let the total points on the remaining 5 quizzes be $x$. She has 92 points on the first 6 quizzes and wants more than 140 for the semester, so $92+x>140$.

Step4: Translate statement 4

Let the width of the rectangle be $x$ inches, then the length is $x + 6$ inches. The perimeter formula is $P=2(l + w)$, and the perimeter is more than 92 inches, so $2((x + 6)+x)>92$.

Answer:

1. $2x+2\geq92$
2. $x+(2x + 6)=92$
3. $92+x>140$
4. $2((x + 6)+x)>92$