Could someone please check my math questions? My answers are under the questions...
32. Six times a number less than ten is eight. Find the number.
a. 1/3
b. 3
c. -1/3
d. -3
My Answer ~ b
33. Jane works at the public library after school. She makes $7.00 per hour. She cannot work more than 15 hours per week. If y = 7x represents Jane's earning, what are the values in the solution set?
a. x < 15
b. 0 < x < 15
c. 1 < x < 15
d. All real numbers
My Answer~ a
Six times a number less than ten
So, is that
(Six times a number) less than ten: 10-6x=8
or Six times (a number less than ten): 6(10-x)=8
?
Either way, it's not 3
You solved
6x-10 = 8
x<15 allows for negative hours. Bzzzt.
The reasonable choice is thus
0 <= x <= 15
But the way the question is worded that is not available. For (b) to be the answer it should have read
Jane must work less than 15 hours per week.
"Not more" is not the same as "less than"
To solve these math questions, we'll break down the information given and follow a step-by-step process.
32. The equation "Six times a number less than ten is eight" can be expressed as 6x < 10 = 8, where x represents the unknown number. We can solve this equation to find the value of x.
First, subtract 8 from both sides of the equation:
6x < 10 - 8
Simplifying the right side:
6x < 2
Now, divide both sides of the equation by 6 to isolate x:
x < 2/6
Simplifying the right side:
x < 1/3
So, the correct answer is option c. -1/3.
33. The given equation "y = 7x" represents Jane's earnings, where y is her total earnings and x is the number of hours she works. The question asks for the range of possible values for x.
Since Jane cannot work more than 15 hours per week, we know that x has to be less than or equal to 15. This eliminates option d.
To determine if x can be 15 or any value less than 15, we need to consider the inequalities in the equation.
The inequality "x < 15" means that x is strictly less than 15, so it does not include the value 15 itself. This eliminates option a.
Therefore, the correct answer is option b. 0 < x < 15, which represents that x must be greater than 0 and less than 15.
So, your answers are as follows:
32. The number is -1/3 (option c).
33. The values in the solution set are 0 < x < 15 (option b).
I hope this helps clarify the solutions to your math questions! Let me know if you have any further inquiries.